1–1
Name
Date
Skills Practice
Chapter Resources
Place Value Through Billions
Name the place value and write the value of the underlined digit.
2. 65,893
1. 2,346
3. 763,406,594
4. 407,356,138,920
5. 64,321,008
6. 117,927,724,417
7. 903,004,200,006
Write each number in standard form.
8. 3 thousand, 125
9. 52 thousand, 40
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write each number in expanded form.
10. 7,450,693
11. 531,017
Write each number in word form.
12. 9,000,000,006
13. 273,273
Solve.
15. Neptune is the planet farthest from the
Sun. It orbits the Sun from a distance
of about 4 billion, 497 million miles.
Write the number in standard form.
14. Mercury is the planet closest to the
Sun. It orbits the Sun from a distance of
about 28 million, 600 thousand miles.
Write the number in standard form.
Grade 5
9
Chapter 1
1–2
Name
Date
Skills Practice
Compare Whole Numbers
with <, >, or = to make a true sentence.
Replace each
1. 1,040
3. 840
10
480
5. 123,778
7. 6,823
2. 14,092
123,778
682
19,812
4. 1,001
101
6. 9,879
9,798
8. 5
13
9. 190
19
10. 71
11. 192
291
12. 611
611
13. 314
3,140
14. 657
567
15. 324
452
98
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
16. Michael ran 7 miles during one week. Krista ran 9 miles during one
week. Who ran more miles?
17. Jerry is 55 inches tall. Tom is 56 inches tall. Who is taller?
Grade 5
14
Chapter 1
1–3
Name
Date
Skills Practice
Problem-Solving Strategy: Use the Four-Step Plan
Solve. Use the four-step plan.
1. The three highest mountains
in Colorado are Mount Massive
(14,421 ft), Mount Harvard (14,420 ft),
and Mount Elbert (14,433 ft). Which
mountain has the greatest height?
2. Hoover Dam, in the United States, is
223 meters high. Ertan Dam, in China,
is 240 meters high. In Canada, Mica
Dam is 243 meters high. List the dams
by height from greatest to least.
3. The Akshi Kaikyo suspension bridge
in Japan has a span of 6,570 feet. The
Humber suspension bridge in England
has a span of 4,626 feet. The Izmit Bay
suspension bridge in Turkey has a span
of 5,538 feet. Which bridge has the
shortest span?
4. There are three long tunnels that go
under Boston Harbor. The Sumner
Tunnel is 5,653 feet long. The Callahan
Tunnel is 5,070 feet long. The Ted
Williams Tunnel is 8,448 feet long. List
the tunnels from shortest to longest.
Grade 5
Land Tunnels in the United States
Tunnel
Liberty Tubes
Devil’s Side
E. Johnson
Memorial
Squirrel Hill
20
State
Pennsylvania
California
Length (ft)
5,920
3,400
Colorado
Pennsylvania
8,959
4,225
Chapter 1
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. List the tunnels in the table at the right
by name in order from shortest to
longest.
1–4
Name
Date
Skills Practice
Represent Decimals
Write each fraction as a decimal.
1.
3
_
2.
498
_
3.
7
_
4.
1
_
5.
947
_
6.
3
_
7.
18
_
8.
1
_
9.
11
_
10.
1
_
11.
256
_
12.
3
_
13.
77
_
14.
3
_
15.
13
_
16.
999
_
17.
9
_
18.
751
_
19.
7
_
20.
2
_
21.
1
_
22.
357
_
23.
4
_
24.
632
_
10
2
25
10
100
1,000
10
1,000
1,000
1,000
5
1,000
5
25
5
5
10
10
20
100
50
1,000
20
1,000
25. The largest butterfly in the world is
found in Papua, New Guinea. The
female of the species weighs about
0.9 ounce. Use a fraction to write the
female’s weight.
Grade 5
26. The shortest fish ever recorded is the
dwarf goby found in the Indo-Pacific.
The female of this species is about
0.35 inch long. Use a fraction to write
the female’s length.
24
Chapter 1
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve.
1–5
Name
Date
Skills Practice
Chapter Resources
Place Value Through Thousandths
Write the place value and the value of each underlined digit.
1. 2.8
2. 1.427
3. 2.531
4. 35.052
5. 5.35
6. 24.002
Write each number in standard form.
7. 5 and 34 thousandths
8. 34 and 12 hundredths
9. 20 + 4 + 0.7 + 0.04 + 0.005
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10. 100 + 7 + 0.05 + 0.007
Write each number in expanded form and word form.
11. 23.5
12. 164.38
13. 4.292
14. 53.007
Grade 5
29
Chapter 1
1–6
Name
Date
Skills Practice
Compare Decimals
Replace each
1. 3.976
3. 126.698
with <, >, or = to make a true sentence.
4.007
2. 89.001
126.689
89.100
4. 5.052
5.052
9.807
5. 3.674
6.764
6. 9.087
7. 0.256
0.256
8. 2.7
9. 6.030
6.03
10. 7.89
7.189
11. 12.54
1.254
12. 0.981
2.3
13. 0.004
0.040
14. 8.26
8.6
15. 5.085
5.805
16. 0.86
0.168
17. 5.309
5.003
2.82
19. In one year Seattle, Washington,
recorded 0.24 inch of snow, and
Chicago, Illinois, recorded 30.9 inches
of snow. Which city had more snow?
18. In January, the average low
temperature in Montreal, Quebec,
Canada, is 5.2°F, and the average low
temperature in Cape Town, South
Africa, is 60.3°F. Which city is warmer
in January?
Grade 5
34
Chapter 1
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve.
1–7
Name
Date
Skills Practice
with>, <, or = to compare each pair of
Replace each
numbers.
1. 3,976
4,007
2.82
1.254
89,100
4. 1,435,052
29,436,764
5. 19,463,674
10. 12.54
2. 89,001
126,689
3. 126,698
7. 2.7
Chapter Resources
Order Whole Numbers and Decimals
145,052
6. 4,303,259,087
4,033,259,807
8. 6.030
6.03
9. 7.89
11. 0.981
2.3
12. 0.004
7.189
0.040
Order each set of numbers from least to greatest.
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
13. 17,639; 3,828; 45,947
14. 890,409; 890,904; 809,904
15. 0.186; 0.1; 0.86; 0.168
16. 5.309; 5.003; 0.53; 0.9
Solve.
17. In January, the average low temperature in Montreal is 5.2°F, and the average low
temperature in Cape Town is 60.3°F. Which city is warmer in January?
18. In one year Seattle recorded 0.24 inches of snow, Chicago recorded 30.9 inches of
snow, and Birmingham recorded 1 inch of snow. Write these amounts in order from
least to greatest.
Grade 5
39
Chapter 1
Date
Skills Practice
Problem-Solving Strategy: Guess and Check
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Use the guess and check strategy to solve.
1. The Bactrian camel has two humps
and the Dromedary camel has one
hump. In a group of 15 camels, the
total number of humps is 21. How
many camels of each type are there?
2. The circus orders bicycles and unicycles
for a new act. It orders a total of
12 cycles. The cycles have 16 tires
altogether. How many bicycles and
unicycles did the circus order?
3. Anja buys a magazine and a pizza.
She spends $8.10. The magazine costs
$2.40 less than the pizza. How much
does the pizza cost?
4. A letter to Europe from the United
States costs $0.80 to mail. A letter
mailed within the United States costs
$0.41. Nancy mails 5 letters for $2.83,
some to Europe and some to the
United States. How many letters did
she send to Europe?
5. Warren spent $8.50 at the store.
He spent $2.40 on paper, $0.88 on
pencils, and $2.65 on markers. He
spent the rest on a notebook. How
much did the notebook cost?
6. Ms. Baxter takes a group of 8 children
to a concert. Tickets for children
12 years and older cost $3.50. Tickets
for children under 12 cost $2.25. She
spends a total of $21.75 on tickets for
the children. How many children are
12 and older?
Grade 5
45
Chapter 1
Chapter Resources
1–8
Name
2–1
Name
Date
Skills Practice
Chapter Resources
Round Whole Numbers and Decimals
Round each decimal to the place indicated.
1. 0.463; tenths
2. 32.877; hundredths
3. 5.65689; thousandths
4. 3.48; ones
5. 56.45; tens
6. 4.67; tenths
7. 13.8908; tenths
8. 21.9; tens
9. The price of a gallon of milk is $3.75. How much is this to the
nearest dollar?
Round each whole number to the place indicated.
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10. 3,579; thousand
11. 29,342; hundred
12. 433,231,292; million
13. 711,900; hundred thousand
14. 33,110; ten thousand
15. 132,509; ten
16. 559,308; ten thousand
17. 14,663; hundred
18. 8,413; thousand
19. There are about 77,621,001 pet cats in the United States. How
many pet cats are there rounded to the nearest hundred thousand?
Grade 5
9
Chapter 2
2–2
Name
Date
Skills Practice
Estimate Sums and Differences
Estimate each sum or difference by rounding.
1. 68.99 + 22.31
2. 39.57 + 18.34
3. 81.25 - 23.16
4. 21.56 - 19.62
5. 34.87 - 29.12
6. 69.45 - 44.8
7. $78.69 + $31.49
8. $258.32 + $378.60
9. 5.69 + 3.47 + 8.02
10. 6.6 + 1.22 + 5.54
12. 9.7325 + 9.55 + 10.333
13. 39.8 + 39.6 + 40.21 + 40.47
14. $69.72 + $70.44 + $70.59 + $69.56
Solve.
15. Miriam bought a basketball for $24.99 and basketball shoes for
$47.79. About how much did Miriam spend on the ball and shoes?
16. Albuquerque gets an average of 6.35 inches of precipitation a year.
Phoenix gets an average of 6.82 inches a year. About how many
more inches of precipitation does Phoenix get than Albuquerque?
Grade 5
14
Chapter 2
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11. $4.56 + $4.79 + $5.21 + $5.38
2–3
Name
Date
Skills Practice
Problem-Solving Strategy: Work Backward
Solve. Use the work backward strategy.
1. Joel spent $6 for a movie ticket and $4
for a drink. He also played some video
games that each cost $2.
2. Patrick arrived at school at 8:30 A.M. If
it took him 45 minutes to get ready,
10 minutes to wait for the school bus,
and 20 minutes to get to school, what
time did he wake up?
He spent $16 in all. How many video
games did he play.
3. Lauro collects baseball cards. He had
a total of 542 cards, but sold some of
them so that he could buy a DVD. He
now has 489 cards.
If he made $106, and he charged the
same amount for each card, how much
did he charge for each card?
If Teresa has a total of 34 birdcages,
how many birds are together in each
cage?
20
How many jars did Julia fill?
jars
How many jars did Mel fill?
jars
How many jars did Paul fill?
jars
Chapter 2
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6. Julia, Paul, and Mel helped their
mother make jelly. Julia filled one third
of the jars, and Paul filled twice as
many as Mel did. They filled a total of
27 jars.
5. Teresa owns a pet shop. She has
24 dogs, 32 cats, 84 lovebirds,
24 parakeets, and 62 canaries. Each
dog has its own cage, and there
are two cats per cage. The birds are
divided equally among the birdcages.
Grade 5
4. Carol is thinking of a number. If
the number is increased by 6, then
doubled, and 9 is subtracted from the
product, the result is 23. What is the
original number?
2–4
Name
Date
Skills Practice
Add and Subtract Whole Numbers
Add or subtract.
1.
9,868
+ 6,329
________
2.
3,136
- 473
________
3.
87
+ 612
______
4.
445
102
______
5.
3,007
1,980
________
6.
4,672
+
1,531
________
7.
31,043
+ 56,691
________
__
8.
285
- 58
______
9.
4,609
- 281
________
10.
124,543
+
96,883
________
___
11.
12,974
+
4,73__
4
________
12.
20,431
17,64__
2
________
13.
5,802
+ 4,289
________
14.
30,048
- 9,33__
8
________
15.
109
- 65
______
17. 1,265 + 877 =
18. 5,954 - 4,883 =
19. 2,980 + 135,618 =
20. 4,465 - 219 =
21. 78,327 - 59,912 =
22. 33 + 579 =
23. 210,336 - 89,481 =
Grade 5
24
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
16. 34,504 + 5,712 =
Chapter 2
2–5
Name
Date
Skills Practice
Problem-Solving Investigation: Estimate or Exact Answer
For each problem, determine whether you need an estimate or an
exact answer. Then solve.
1. The ski team has a race at 9:00 A.M.
The race is 120 miles away. The team
leaves at 6:00 A.M. and drives about
50 miles each hour. Will they arrive
at the race on time?
2. The ski team travels in 4 vans. Each
van holds 9 team members. How
many members are on the team?
3. School raffle tickets cost $8 apiece. The
school's goal is to raise at least $3,000
from the raffle. If 424 tickets are sold,
will the school meet its goal?
4. Students at Tuscan School filled out
a survey. The survey showed that of
374 students, 195 speak a second
language. How many students speak
only one language?
Grade 5
6. At the beginning of the last year,
there were 368 students at the
elementary school. By the beginning
of this year, 72 of those students
had moved. About how many
students started the school year this
year?
30
Chapter 2
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Book World receives 12 boxes of
books. Each box contains 16 copies
of the new best-seller, Norton's Last
Laugh. How many copies of Norton's
Last Laugh does the store receive?
2–6
Name
Date
Skills Practice
Add and Subtract Decimals
Add or subtract.
1.
9.868
+ 6.329
________
2.
3.136
2.473
________
3.
0.87
+
6.12
_______
4.
4.45
1.02
_______
5.
3.007
- 1.980
________
6.
4.672
+
15.31
________
7.
31.043
+
56.691
_________
8.
2.85
0.58
_______
9.
4.609
2.81
________
10.
124.543
+
96.883
__________
11.
12.974
+
4.734
_________
12.
20.431
17.642
_________
13.
5.8
+ 4.289
________
14.
30.048
9.338
_________
15.
$1.09
0.65
_______
16.
76.509
+
120.306
__________
17.
321.658
- 197.369
__________
18.
3.472
+
7.810
________
19.
3.65
0.824
________
20.
$28.99
+
1.75
_________
22. 1.265 + 8.77 =
23. 9.54 - 4.883 =
24. 2.980 + 135.618 =
25. $44.65 - $2.19 =
26. 78.327 - 59.912 =
27. $0.33 + $5.79 =
28. 210.336 - 89.481 =
Solve.
29. Gasoline prices are given to the nearest
thousandth of a dollar. If gasoline rises
in price from $1.499 to $1.589, what is
the amount of the increase?
Grade 5
30. The area of Max’s room, including his
closet, is 695.676 square feet. The
area of his closet is 10.463 square
feet. What is the area of his room, not
including the closet?
34
Chapter 2
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
21. 34.504 + 5.712 =
2–7
Name
Date
Skills Practice
Chapter Resources
Addition Properties
Identify the addition property used to rewrite each problem.
1. 7 + (26 + 13) = (7 + 26) + 13
2. 18 + 12 + 7 = 12 + 7 + 18
3. 57 + 0 = 57
4. 22 + 5 + 3 = 3 + 22 + 5
Use properties of addition to find each sum mentally. Show your
steps and identify the properties that you used.
5. 15 + 5 + 6
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6. 12 + 18 + 7
7. 4.3 + 1 + 5.7
For exercises 8–9, find the value that makes the sentence true.
8. 45 + (10 + 34) = (10 +
) + 34
9. 1.1 + (3.9 + 12) = (3.9 + 1.1) +
Solve.
10. Sasha spent $1.05 on a soda, $5.25 on a sandwich, $0.75 on a piece of fruit, and
$4.95 on a magazine. Use mental math to find the total amount she spent.
Grade 5
39
Chapter 2
2–8
Name
Date
Skills Practice
Add and Subtract Mentally
Add or subtract mentally. Use compensation.
1. 46 + 27
2. 9.4 + 1.8
3. 647 - 498
4. 26.4 - 20.1
5. 171 + 204
6. 7.4 - 1.3
7. 105 + 278
8. 347 + 8.9
9. 415 - 196
10. 51.3 - 23.7
12. 9.5 - 1.4
13. 56 + 24
14. 7.2 + 3.9
15. 216 - 173
16. 42.8 - 25.3
17. 369 + 76
18. 25.4 - 11.7
Solve.
19. Sarah skipped rope 335 times in a
row. Katie skipped rope 296 times in
a row. Use mental math to find how
many times more Sarah skipped rope
than Katie.
Grade 5
20. When Jonah was born, he weighed
7.4 pounds. His twin brother, James,
weighed 7.8 pounds when he was
born. Use mental math to find how
much they weighed altogether.
44
Chapter 2
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11. 309 + 265
3–1
Name
Date
Skills Practice
Chapter Resources
Multiplication Patterns
Find each product mentally.
1. 8 × 2=
3. 4 × 5 =
8 × 20 =
6 × 40 =
4 × 50 =
8 × 200 =
6 × 400 =
4 × 500 =
8 × 2,000 =
6 × 4,000 =
4 × 5,000 =
4. 3 × 80 =
5. 5 × 60 =
6. 9 × $70 =
30 × 80 =
50 × 60 =
90 × $70 =
300 × 80 =
500 × 60 =
900 × $70 =
3,000 × 80 =
5,000 × 60 =
9,000 × $70 =
7. 90 × 3 =
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. 6 × 4 =
8. 7 × $4,000 =
9. 200 × 6 =
10. 30 × 40 =
11. 600 × 70 =
12. 40 × 800 =
13. 4 × $1,000 =
14. 500 × 80 =
15. 70 × 100 =
16. 3 × 30 =
17. 5 × 1,000 =
18. 7 × $900 =
19. 50 × 80 =
20. 100 × 80 =
21. 50 × 20 =
Solve.
22. The 9 members of a music club in
Indianapolis want to fly to New York
to see several musicals. The cost of a
round trip ticket is $300. How much
would the airfare be altogether?
Grade 5
23. During one week, an airport shop
sold 70 New York City travel guides
for $9 each. How much was the total
received for the guides?
9
Chapter 3
3–2
Name
Date
Skills Practice
The Distributive Property
Find each product mentally using the Distributive Property. Show
the steps that you used.
1. 7 × 19
2. 2 × 27
3. 6 × 88
4. 9 × 98
5. 3 × 13
6. 8 × 68
7. 7 × 32
8. 9 × 35
9. 8 × 17
10. 4 × 71
Solve.
11. Each of 6 hikers were allowed to bring
24 pounds of gear on a cross-country
hike. How many pounds of gear was
that altogether?
Grade 5
12. The hikers plan to travel an average
of 12 miles each day for 9 days. How
many miles do they plan to travel in
all?
14
Chapter 3
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Rewrite each expression using the Distributive Property. Then
evaluate.
3–3
Name
Date
Skills Practice
Chapter Resources
Estimate Products
Estimate by rounding. Show your work.
1. 34 × 10
2. 59 × 32
3. 446 × 682
4. 21 × 663
5. 98 × 32
6. 91 × 32
7. 334 × 847
8. 929 × 8
9. 43 × 58
10. 186 × 92
11. 342 × 86
12. 396 × 23
13.
8,547
× 836
14.
603
15.
× 29
408
16.
× 46
3,045
×
38
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Estimate by using compatible numbers. Show your work.
17. 6 × 24
18. 8 × 48
19. 12 × 26
20. 12 × 52
21. 110 × 97
22. 120 × 11
Solve.
23. Tickets to a basketball game cost $22
each. Mr. Reynolds bought 17 tickets
to give away as prizes at an assembly.
About how much did the tickets cost
altogether?
Grade 5
24. There are 514 students at Scioto
Elementary. Each of the students
donated 7 food items for a charity food
drive. About how many items were
collected altogether?
19
Chapter 3
Name
3–4
Date
Skills Practice
Multiply by One-Digit Numbers
Multiply.
1.
83
2.
× 5
5.
56
6.
14
7.
4
14.
8.
7
15.
12.
3
312
×
3
769
×
89
× 2
645
×
44
× 3
28
11.
6
623
×
4.
×4
732
×
9
13. 564
×
10.
32
×4
× 7
557
×
3.
× 6
× 5
9.
66
16.
2
293
×
6
18. 19 × 8
19. 344 × 7
20. 3 × 51
21. 2 × 99
22. 63 × 3
23. 519 × 4
24. 4 × 89
25. 2 × 67
26. 42 × 5
27. 716 × 8
28. 6 × 191
29. The math club at Southview
Elementary School sold 443 rolls of
wrapping paper during the holiday
fundraiser. If the price of each roll was
$4, how much money did they earn?
Grade 5
30. Andrea made 28 flowerpots to sell
at the craft fair. Jenna made twice as
many flowerpots. How many flower
pots does Jenna have?
24
Chapter 3
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
17. 4 × 39
3–5
Name
Date
Skills Practice
Problem-Solving Strategy: Draw a picture
Solve. Use the draw a picture strategy.
2. Jack builds a patio from square tiles
that are 2 feet on each side. The patio
is 10 feet by 16 feet. How many tiles
does Jack need in order to build the
patio?
3. Howard leaves the dock and sails 2.5
miles west. He turns south and sails
3.5 miles. Then he turns east and sails
2.5 miles. In what direction should
Howard turn if he wants to use the
most direct route to return to the
dock? If Howard uses this route, how
many miles will he have sailed in all?
4. The main lawn of a college is a
rectangle with one building on each
side. There is a path from each
building to each of the other buildings.
How many paths are there?
5. Akira cut triangles of the same size out
of different colors of cloth. She is going
to use the pieces to make a quilt. She
places the triangles together around
one point until they form a hexagon.
How many of the triangles did she
have to use?
6. For every two steps her dad takes,
Heidi takes 4 steps. How many steps
will she takes if her dad takes 30
steps?
Grade 5
30
Chapter 3
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. Maria wants to tack three rectangular
pictures in a row on the bulletin board.
The edges of the pictures can overlap.
Maria wants to put a tack in each
corner of each picture. How many
tacks does she need?
Name
3–6
Date
Skills Practice
Multiply by Two-Digit Numbers
Multiply.
1. 32 × 517 =
2. 466 × 21 =
3. 83 × 13 =
4. 43 × 65 =
5. 458 × 26 =
6. 329 × 72 =
7. 601 × 24 =
8. 728 × 68 =
9. 188 × 46 =
10. 250 × 27 =
11. 45 × 371 =
12. 70 × 686 =
13.
67
14.
× 211
18.
$740
×
× 456
19.
24.
× 700
28.
176
× 45
92
318
20.
500
× 19
16.
25.
262
21.
17.
114
202
26.
79
22.
31.
× 67
82
× 820
653
× 20
27.
× 349
241
345
× 42
× 48
× 96
30.
824
× 19
× 39
× 52
29.
170
× 55
× 301
16
49
15.
26
× 781
32.
199
× 36
Solve.
33. A basketball player scored an average
of 23 points per game. He played 82
games during the season. How many
points did he score that season?
Grade 5
34. A basketball arena has 36 sections of
seats. Each section contains 784 seats.
How many people can the arena seat?
34
Chapter 3
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
23.
30
Date
Skills Practice
Multiplication Properties
Identify the multiplication property used to rewrite each problem.
1. (185 × 6) ×
3. 124 ×
= 185 × (6 × 2)
2. 9 × (60 + 7) = (
= 14 × 124
4. 3.41 ×
× 60) + (9 × 7)
= 3.41
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Use properties of multiplication to find each product mentally.
Show your steps and identify the properties that you used.
5. 5 × 24 × 2
6. 200 × (4 × 7)
7. 483 × 10 × 1
8. 5 × 3 × 20
Grade 5
39
Chapter 3
Chapter Resources
3–7
Name
Name
3–8
Date
Skills Practice
Extending Multiplication
Estimate each product.
1.
$1.80
×
4.
$31.15
×
10.
5.
8.
× 31
15
14.7
× 305
104.6
15.
× 411
21.3
× 72
Solve.
16. Each Sunday during his nine week
summer vacation, Ray buys a
newspaper. The Sunday paper costs
$1.85. About how much did Ray spend
on the Sunday newspaper during his
vacation?
Grade 5
17. Jorge buys 8 pounds of ground beef
for $3.29 a pound. About how much
did he pay altogether?
44
Chapter 3
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
× 31
14.
12.
4
$9.72
×
14
× 41
42.3
9.
4
$1.67
×
$2.26
11. 48.2
13.
6.
5
8.4
$14.75
×
$4.80
×
6
3.
7
×
4
$1.79
$2.83
×
8
×
7.
2.
3–9
Name
Date
Skills Practice
Problem-Solving Investigation: Extra or Missing Information
Solve each problem. If there is extra information, identify it. If
there is not enough information, tell what information is needed.
1. Mrs. Blackwell gives each of her students two pencils. How many
pencils did she hand out?
2. Mary has saved $50. If she wants to buy an mp3 player that costs
$250, will she have enough money in six months?
3. Marco does 10 extra math problems each school night. How many
extra problems does he do each school week?
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. Juan’s family is from Houston. They want to go to Florida for
vacation. If they need $100 for each person in the family in order to
be able to make the trip, will they have enough?
5. Shannon has five red shirts, three blue shirts, and four purple shirts.
She has three more white shirts than she does brown shirts. How
many brown shirts does she have?
6. If David plays 3 tennis matches every week for 9 weeks, how many
matches will he play altogether?
Grade 5
50
Chapter 3
Date
Skills Practice
Division Patterns
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Divide mentally.
1. 210 ÷ 3 =
2. 560 ÷ 7 =
3. 500 ÷ 5 =
4. 360 ÷ 6 =
5. 100 ÷ 2 =
6. 250 ÷ 5 =
7. 140 ÷ 2 =
8. 280 ÷ 4 =
9. 720 ÷ 9 =
10. 180 ÷ 3 =
11. 480 ÷ 8 =
12. 360 ÷ 4 =
13. 350 ÷ 5 =
14. 450 ÷ 9 =
15. 700 ÷ 10 =
16. 480 ÷ 12 =
17. 8 640
18. 4 320
19. 9 900
20. 9 360
21. 11 990
22. 3 240
23. 5 300
24. 2 180
25. 9 990
26. 7 630
27. 6 420
28. 8 400
29. 4 2,400
30. 8 3,200
31. 6 6,000
32. 9 810
33. 5 4,000
34. 10 5,000
35. 7 490
36. 9 450
Solve.
37. Corey has saved 60 files on the hard
drive of his computer. He wants to
divide them equally among 10 folders.
How many files will go in each folder?
38. Jasmine has 50 computer disks.
She has just enough cases to place
5 disks in each case. How many cases
does she have?
39. Ten friends paid a total of $80 for
movie tickets. How much did one
movie ticket cost?
40. The Millers drove 300 miles in two
days. On average, how many miles did
they drive each day?
Grade 5
9
Chapter 4
Chapter Resources
4–1
Name
4–2
Name
Date
Skills Practice
Estimate Quotients
Estimate. Show your work.
1. 2,117 ÷ 7
2. 2,001 ÷ 19
3. 2,100 ÷ 708
4. 540 ÷ 90
5. 270 ÷ 9
6. 3,515 ÷ 49
7. 1,621 ÷ 19
8. 3,493 ÷ 698
9. 6,028 ÷ 293
10. 8,405 ÷ 121
12. 45,112 ÷ 5,010
13. 6,000 ÷ 48
14. 1,800 ÷ 27
15. 4,200 ÷ 60
16. 150,175 ÷ 3
17. 480,000 ÷ 59,997
18. 18,106 ÷ 289
19. 717 ÷ 9
20. 638 ÷ 8
21. 463 ÷ 90
22. 249 ÷ 81
23. 162 ÷ 4
24. 534 ÷ 9
25. 481 ÷ 64
26. 34 ÷ 4
27. 57 ÷ 9
28. 468 ÷ 8
29. 409 ÷ 48
30. 363 ÷ 3
31. 311 ÷ 5
32. 364 ÷ 69
Solve.
33.
Jane makes 20 equal payments to buy
a CD player that sells for $170. About
how much is each payment? Show
your work.
Grade 5
34. Justine makes 30 equal payments to
buy a car that sells for $14,000. About
how much is each payment? Show
your work.
14
Chapter 4
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11. 15,997 ÷ 395
4–3
Name
Date
Skills Practice
Chapter Resources
Divide by One-Digit Numbers
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Divide.
1. 3 385
2. 7 511
3. 9 179
4. 5 254
407
5. 6 6. 8 167
7. 4 131
8. 9 852
123
9. 5 10. 3 304
11. 7 224
12. 9 782
13. 4 299
14. 8 207
15. 5 632
16. 3 819
17. 463 ÷ 5 =
18. 606 ÷ 8 =
19. 615 ÷ 2 =
20. 103 ÷ 9 =
21. 618 ÷ 3 =
22. 968 ÷ 6 =
23. 53 ÷ 2 =
24. 55 ÷ 4 =
25. 27 ÷ 8 =
26. 98 ÷ 3 =
27. 22 ÷ 9 =
28. 54 ÷ 5 =
Solve.
29. The driving distance between
Lakeview and Glendale is 600 miles.
You make the drive in 4 days and
drive the same number of miles each
day. How many miles do you drive
each day?
Grade 5
30. The distance from Springfield to Pine
Ridge and back is 600 miles. You
drive from Springfield to Pine Ridge
to Springfield in July. Your car gets
30 miles for each gallon of gas it uses.
To the nearest gallon, how many
gallons did you use?
19
Chapter 4
4–4
Name
Date
Skills Practice
Divide by Two-Digit Numbers
Divide.
1. 58 94
2. 78 161
3. 23 491
4. 47 539
5. 21 390
6. 96 694
521
7. 73 8. 88 755
9. 39 388
10. 37 120
11. 54 254
12. 82 215
275
13. 84 14. 22 416
15. 32 224
17. 649 ÷ 84 =
18. 129 ÷ 95 =
19. 720 ÷ 45 =
20. 201 ÷ 70 =
21. 639 ÷ 87 =
22. 488 ÷ 96 =
23. 289 ÷ 54 =
24. 205 ÷ 75 =
25. 878 ÷ 42 =
Solve.
26. Members of the Bladerunners skating
club collected $950 from fundraising
activities. They want to buy Ultrablade
skates, which are $50 a pair. How
many pairs of skates can they buy?
Grade 5
27. Emily read 124 hours in January. If
she read an equal number of hours
each day, how many hours did she
read each day?
24
Chapter 4
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
16. 204 ÷ 33 =
4–5
Name
Date
Skills Practice
Problem-Solving Strategy: Act It Out
Solve. Use the act it out strategy.
1. The ceramics class is designing mugs with three colored stripes.
The colors are red, yellow, and green. How many different ways can
students in the class arrange the three colored stripes?
2. Meg and Matt are painting all 4 walls of a room. Each person is
1
painting 2 walls. After one hour, Meg has painted _ of one wall,
2
and Matt has painted 1 wall. How much longer will it take Meg to
paint her 2 walls than it will take Matt to paint his?
3. Twenty-four students are in study hall. Eight more arrive. At the
same time, 12 leave. Then, 16 leave and 8 more arrive. How many
students are left in study hall?
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. Ellen is decorating a wall with family pictures. She has 2 different
pictures that are 10 inches and 2 different pictures that are 8 inches.
If she keeps all the pictures in one row, how many ways can she
arrange the pictures?
5. Dolores has 6 quarters, 5 dimes, 4 nickels, and 10 pennies. How
many different combinations of coins can she make to have $1?
Grade 5
30
Chapter 4
4–6
Name
Date
Skills Practice
Interpret the Remainder
Solve. Explain how you interpreted the remainder.
2. Students from four local schools are
bussed to the Science Fair. The number
of students and teachers attending is
290. Each bus holds 50 passengers.
How many buses will be needed?
3. The Natural History Museum is open
10 hours each day. A 9-minute movie
about dinosaurs plays continuously.
How many times does the complete
movie play each day? (Hint: 10 hours
= 600 minutes)
4. The Natural History Museum sells
postcards for $3 each. Morris has $29
to spend. If he buys as many postcards
as he can, how much money will he
have left?
5. A museum curator has 203 wildlife
photographs. She wants to display
them in groups of 8. How many groups
of 8 can she make?
6. Each museum tour can have a
maximum of 20 people. There are
110 students and teachers who want
to take a tour. How many groups will
they need?
7. An artist makes models of dinosaurs.
He has 59 dinosaurs. He packages
them in boxes of 4. After the artist fills
as many boxes as he can, how many
dinosaurs will be left?
8. At the Discovery Center, students work
in groups of 5 or fewer. There are 89
students who want to use the center.
What is the least number of groups
that will need to be formed?
Grade 5
34
Chapter 4
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. At the Science Fair, a hall featuring an
electronics exhibit holds 30 people.
How many groups will need to be
formed if 460 people want to see the
electronics exhibit?
4–7
Name
Date
Skills Practice
Chapter Resources
Extending Division
Estimate each quotient.
1. 21.9 ÷ 3
2. 36.3 ÷ 6
3. 12.5 ÷ 5
4. 17.2 ÷ 8
5. 23.7 ÷ 6
6. 20.6 ÷ 4
7. 24.3 ÷ 8
8. 118.1 ÷ 10
9. 13.2 ÷ 6
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10. 32.3 ÷ 3
11. 65.1 ÷ 2
12. 13.5 ÷ 5
13. $18.01 ÷ 9 =
14. $16.48 ÷ 4 =
15. $13.64 ÷ 7 =
16. $240.50 ÷ 6 =
17. $62.70 ÷ 8 =
18. $22.90 ÷ 7 =
19. $30.87 ÷ 4 =
20. $44.40 ÷ 5 =
Solve.
21. Nine students each ordered a different
meal from a fast food restaurant as
part of a science project. When they
finished eating, they weighed all
the packaging. They found that the
packaging weighed a total of 46.1
ounces. Estimate the average weight of
the packaging from each meal.
Grade 5
22. Population density is found by dividing
the number of people by the area.
Pecos County, Texas, has a population
of 16,039 and a land area of 4,764
square miles. Estimate the population
density of Pecos County. Then use a
calculator to find the exact answer
rounded to the nearest whole number.
39
Chapter 4
Date
Skills Practice
Problem-Solving Investigation: Choose the Best Strategy
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve. Use any strategy shown below to solve each problem.
• Draw a picture
• Work backward
• Guess and check
• Act it out
1. Kelly buys 12 packs of postcards and
3 packs of souvenir photos while on
vacation. One pack of postcards costs
$3. Kelly spends $54 total. How much
does each pack of souvenir photos
cost?
2. 58 passengers each checked 2 pieces of
luggage at the airport. 122 passengers
each checked 1 piece of luggage.
How many pieces of luggage did the
passengers check in all? If the plane
holds 250 pieces of luggage, will there
be enough room for the luggage the
passengers checked?
3. Mr. Stinson took his classes to the
community theater for a play. Mr.
Stinson spent $290 on tickets. Adult
tickets cost $8 and student tickets
cost $5. If Mr. Stinson brought 4 adult
chaperones along, how many students
went to the play?
4. It is 11:30 A.M. and Patrick needs to
finish reading a 145-page book before
returning it to the library at 6:30 P.M.
Patrick has already read 54 pages of the
book. How many pages an hour does
he need to read to return the book on
time?
5. Madeline is saving up to buy a new
pair of rollerblades. The rollerblades she
would like to buy cost $90. She has $34
saved from her birthday. She needs to
earn the rest of the money by saving
her weekly allowance. If she earns $7
a week, how many weeks will she
need to save her allowance to buy the
rollerblades?
6. Mario is packing his backpack for a
camping trip. He has to fit a flashlight,
a bag of snacks, a compass, a water
bottle, a nature guidebook, and a
sweatshirt in to his backpack. The
sweatshirt must go in the bag first.
In how many different ways can the
remaining items go into the backpack?
Grade 5
45
Chapter 4
Chapter Resources
4–8
Name
5–1
Name
Date
Skills Practice
Chapter Resources
Addition Expressions
Evaluate each expression if x = 6 and y = 4.
1. x + 1
2. 9 + y
3. 17 + y
4. y + 19
5. 12 + x
6. 15 + x
7. 7 + x
8. y + 3
9. x + 9
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write an expression for each real-world situation. Then evaluate.
10. John worked x hours planting bushes.
Kim worked 2 more hours than John.
If x = 5, how many hours did Kim
work?
11. A rose bush costs x dollars. A lilac
bush costs $2.50 more than a rose
bush. If x = 40, how much does a
lilac bush cost, in dollars?
12. The lilac bush is x feet tall now. By
next year, it should be 3 feet taller. If
x = 3, how tall will the lilac bush be
then, in feet?
13. John has planted x bushes. He
needs to plant 8 more. If x = 10,
how many bushes will John plant
altogether?
Solve.
15. Last year the troop planted 12
bushes. Evaluate the expression you
wrote in problem 14 to find how
many bushes they planted this year.
14. This year the troop planted 15 more
bushes than last year. Write an
expression for the number planted
this year. Let y represent the number
planted last year.
Grade 5
9
Chapter 5
Date
Skills Practice
Problem-Solving Strategy: Solve a Simpler Problem
Solve a Simpler Problem
Solve. Use the solve a simpler problem strategy.
1. What is the area of the fenced-in
garden shown in the plan below?
2. How much wood is needed to make
the deck shown in the plan below?
12 m
9 ft
5 ft
5m
3 ft
2 ft
9m
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3 ft
4m
4m
9 ft
3m
3. Five farmers can plow five fields in
five hours. How many fields can ten
farmers plow in ten hours?
4. Enriqué has a board that is 20 feet
long. He needs to cut it into 2 foot
long pieces to make shelves. How
many shelves can he make from the
board he has?
5. Constance is cutting ribbon to make
bows to put on gift boxes. The roll of
ribbon she has is 3 feet long. Each
ribbon needs to be 6 inches long. How
many 6 inch bows can she make?
(Hint: 1 foot = 12 inches.)
6. Four people can make 8 bracelets in
one hour. How many bracelets can
12 people working at the same rate
1
make in a _ hour?
2
7. The total land area of four states is
listed in the table. How much greater
is the area of New Hampshire than the
other states combined?
Grade 5
State
15
Total Land Area
(square miles)
Delaware
1,955
New Hampshire
8,969
Rhode Island
1,045
Connecticut
4,845
Chapter 5
Chapter Resources
5–2
Name
5–3
Name
Date
Skills Practice
Chapter Resources
Multiplication Expressions
Evaluate each expression if x = 5 and y = 8.
1. 6x
2. 10x
3. 7y
4. 3y
5. 8x
6. 4x
7. 2x
8. 5y
9. 9y
Evaluate each expression if a = 9 and b = 3.
10. 11a
11. 2a
12. 4b
13. 6b
14. 12b
15. 6a
16. 4a
17. 9b
18. 7b
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write an expression for each real-world situation. Then evaluate.
19. Every year the school’s Science Club
builds b bird feeders. If b = 7, how
many bird feeders will the club build
in 3 years?
20. A hiker walks 3 miles per hour. He
walks for y hours. If y = 9, how many
miles does the hiker walk?
21. Scott kicked g field goals this football
season. Each field goal is 3 points.
If g = 5, how many points did
Scott score?
22. Used DVDs are on sale for $8 each.
Sandra bought d DVDs. If d = 5, how
much did Sandra spend for DVDs?
Grade 5
19
Chapter 5
5–4
Name
Date
Skills Practice
More Algebraic Expressions
Complete the table.
Algebraic
Expressions
Variables
Numbers
Operations
1. 5d + 2c
2. 5w - 4y
3. xy ÷ 4
Evaluate each expression if a = 3 and b = 4.
4. 10 + b
5. 2a + 8
6. 4b - 5a
7. a × b
8. 7a × 9b
9. 8a - 9
10. 18 ÷ 2a
11. ab ÷ 3
12. 15a - 4b
13. ab + 7
14. 36 ÷ 6a
15. 7a + 8b
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Evaluate each expression if x = 7, y = 15, and z = 8.
16. x + y + z
17. x + 2z
18. xz + 3y
19. 4x - 3z
20. xz ÷ 4
21. 6z - 5z
22. 9y ÷ 3
23. 15y + x
24. xy + 2z
25. 13y - zx
26. xz - 2y
27. 3y × 40x
Grade 5
24
Chapter 5
5–5
Name
Date
Skills Practice
Problem-Solving Investigation: Choose the Best Strategy
Use any strategy shown below to solve each problem.
• Act it out
• Look for a pattern
• Make a table
1. To train for the bicycle race, Dan plans to ride 10 miles per day the
first week, adding 3 miles per day each week. How many miles will
he ride per day the eighth week?
2. A rancher is building a square corral with sides that are 20 feet
long. He plans to put a post every 5 feet around the edge of the
corral. How many posts will he need?
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. At 5:00 P.M., the temperature was 24°C. By 8:00 P.M., the temperature
had dropped 6°C. What was the temperature at 8:00 P.M.?
4. Write a problem that you can solve using a problem-solving strategy.
What strategy would you use to solve the problem? Explain why you
chose that strategy.
Grade 5
30
Chapter 5
5–6
Name
Date
Skills Practice
Function Tables
Use the information below to answer Exercises 1 and 2.
Beth has 7 more model horses than her friend Jasmine.
1. Find the function rule.
2. Make a function table to find how many model horses Beth has if
Jasmine has 11, 13, or 15 horses.
Input ( j )
Output
3. Marie is sending books to her cousin. Each book weighs 4 ounces.
Find the function rule. Then make a function table to find how
many ounces 5, 6, or 7 books would weigh.
Input (b)
Output
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. Steven is ordering puzzles for his friends. Each puzzle costs $12.
Find the function rule. Then make a frequency table to find how
much 4, 5, or 6 puzzles would cost.
Input ( p)
Grade 5
Output
34
Chapter 5
5–7
Name
Date
Skills Practice
Chapter Resources
Number Sentences
Find the value of each expression.
1. 44 + (7 × 3)
2. 48 ÷ (8 - 2)
3. (3 + 4) × 8
4. (18 + 12) ÷ (2 + 3)
5. (4 × 2) - 7
6. (6 ÷ 3) + (8 × 5)
7. (3 + 2) × 3
8. (24 ÷ 6) × (3 + 52)
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9. (2 × 5) - (3 × 3)
10. 96 ÷ (3 × 4)
11. (100 - 8) + (4 ÷ 4)
12. (200 - 50) ÷ (12 - 9)
13. 47 + (3 × 11) - (36 ÷ 3)
14. (7 + 6) × (7 - 3)
Solve.
15. Tickets to the school play cost $4 for adults and $2 for students. If 255 adults and
382 students attended the play, write an expression that shows the total amount of
money made on ticket sales. Then evaluate the expression.
16. At the school play, popcorn costs $1 and juice costs $2. Suppose 235 people buy
popcorn and 140 people buy juice. Write an expression that shows the total amount
of money made by selling refreshments. Then simplify the expression.
Grade 5
39
Chapter 5
6–1
Name
Date
Skills Practice
Chapter Resources
Addition and Subtraction Equations
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve each equation. Check your solution.
1. a + 8 = 23
2. s + 9 = 26
3. f + 36 = 58
4. z + 16 = 59
5. v + 14 = 162
6. h + 2 = 3
7. k + 60 = 84
8. t + 30 = 94
9. r + 3 = 17
10. 96 = d + 78
11. s + 15 = 32
12. 100 = c + 42
13. a - 7 = 4
14. v - 9 = 25
15. 96 = i - 3
16. 30 + a = 51
17. 16 + v = 24
18. 3 = n - 1
19. e - 9 = 23
20. 9 + b = 18
21. 6 + a = 13
22. c - 0 = 4
23. 298 = i - 1
24. 17 = r – 4
Solve.
25. The high temperature one day in
Washington, D.C., was 40°F. That was
14°F greater than the low temperature.
Write an addition equation to describe
the situation. Use t to represent the
low temperature. Then solve the
equation.
Grade 5
26. A chapter has 45 pages. Larry has read
n pages, and has 8 pages left. Write a
subtraction equation to represent this
situation. Then solve the equation to
find the number of pages Larry has left
to read.
9
Chapter 6
6–2
Name
Date
Skills Practice
Multiplication Equations
Solve each equation. Check your solution.
2. 6q = 108
3. 20d = 180
4. 6a = 12
5. 4e = 276
6. 15y = 45
7. 8k = 40
8. 4p = 16
9. 3j = 39
10. 12s = 60
11. 30h = 60
12. 8w = 64
13. 3y = 12
14. 2c = 120
15. 10x = 20
16. 7s = 21
17. 4x = 12
18. 32f = 64
19. 6t = 60
20. 4w = 24
Solve.
21. The Martinez family paid $40 for
5 movie passes. Write a multiplication
equation to describe the situation.
Solve it to find the cost in dollars, c,
of each movie pass.
Grade 5
22. Three friends each bought a gift. Each
of the presents cost the same amount.
Together, they paid $15. Write a
multiplication equation to describe the
situation.
14
Chapter 6
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. 7w = 28
6–3
Name
Date
Skills Practice
Problem-Solving Strategy: Make a Table
Use the make a table strategy to solve.
A card shop recorded how many packs
of trading cards it sold each day.
Trading Cards Sold
1. In which week did they sell the most
packs of cards?
Day
Mon.
Tue.
Wed.
Thur.
Fri.
2. In which week did they sell the least
amount?
Week 2
48
43
45
41
39
Week 3
25
37
42
35
41
Bookstore Sales
Month Copies Month Copies
1
26
5
38
2
24
6
19
3
32
7
15
4
18
8
30
3. A bookstore records 8 months
of sales of The Lion, the Witch, and
the Wardrobe, by C.S. Lewis. Did
they sell more books in the first
four months or the last four months?
Blue
Red
Blue
Purple
Blue
20
Favorite Colors
Green Blue
Brown Purple
Pink
Red
Blue
Red
Green Red
Yellow
Pink
Green
Brown
Pink
Chapter 6
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. Joseph took a survey of his
classmates to find their favorite color.
The results are shown in the table to
the right. How many students chose
blue as their favorite color?
Grade 5
Week 1
28
32
38
44
36
6–4
Name
Date
Skills Practice
Geometry: Ordered Pairs
Name the ordered pair for each point.
1. A
2. B
3. C
y
8
C D
7
I
6
K
5
L B
4
G
A
3
H
2
J
E
1
F
x
O 1 2 3 4 5 6 7
4. D
5. E
6. F
Name the point for each ordered pair.
7. (5, 3)
8. (4, 6)
9. (4, 4)
10. (2, 4)
11. (2, 6)
For Exercises 13-16, use the map of the city square at
the right.
y
13. What is located at (3, 6)?
14. Write the ordered pair for the bookstore.
15. If the y-coordinate of the grocery store was moved up
4 units, what would be the ordered pair of the
grocery store?
7
6
5
4
3
2
1
O
Playground
Fountain
Bookstore
Bank
Grocery Store
1 2 3 4 5 6
x
16. Suppose point (4, 2) was moved 2 units to the
left and moved 3 units up. Write the new
ordered pair.
Grade 5
24
Chapter 6
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12. (6, 2)
Name
6–5
Date
Skills Practice
Graph and label each point on the coordinate grid.
1. A (5, 9)
2. I (7, 2)
3. F (0, 4)
4. L (9, 8)
5. G (0, 7)
6. D (6, 6)
7. H (8, 5)
8. B (4, 4)
9. E (2, 7)
10. K (7, 0)
11. C (3, 9)
12. J (9, 9)
Chapter Resources
Algebra and Geometry: Graph Functions
10
9
8
7
6
5
4
3
2
1
O 1 2 3 4 5 6 7 8 9 10
Complete each table using the function represented
in the equation. Then graph the ordered pairs.
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
13. h = 3c
h
c
h
0
0
1
3
2
6
3
9
15. s = 2t + 6
t
s
0
1
2
3
8
14. b = 2a - 1
8
7
6
5
4
3
2
1
O 1 2 3 4 5 6 7 8 c
s
a
b
1
1
2
3
3
b
6
5
4
3
2
1
O 1 2 3 4 5 6 a
4
16. q = 2m
9
8
7
6
5
4
3
2
1
m
q
0
1
2
4
q
6
5
4
3
2
1
O
1 2 3 4 5 6
m
3
O 1 2 3 4 5 6 7 8 9 t
A fifth-grade class checks the pond water in the school’s nature center.
Each day they collect some 4-ounce samples of water and one 8-ounce
sample of water.
17. Write an equation that describes the
18. What is the total amount of water that
relationship between the total ounces
will be collected if students collect
of water collected, w, and the number
three 4-ounce samples?
of 4-ounce samples, s.
Grade 5
29
Chapter 6
6–6
Name
Date
Skills Practice
Functions and Equations
Complete the table. Write an equation to show the relationship.
1.
2.
3.
4
Input
x
0
1
2
3
Output
y
1
3
5
7
Input
x
0
1
2
3
Output
y
3
4
5
6
Input
x
0
1
2
3
Output
y
1
4
7
10
Input
x
0
1
2
3
Output
y
5
7
9
11
4
5
4
5
4
5
4
5
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write an equation for the function described in words. Tell what
each variable in the equation represents.
5. The width of a certain rectangle is 4 times its length.
6. The length of a certain rectangle is 2 times its width.
7. The length in inches of a pencil is equal to 2.54 times its length
in centimeters.
Grade 5
34
Chapter 6
6–7
Name
Date
Skills Practice
Problem-Solving Investigation: Choose the Best Strategy
Use any strategy shown below to solve.
• Use logical reasoning
• Work backward
• Guess and check
2. A scuba diver descended 8 feet below
the surface of the water. Then he
descended an additional 12 feet. He
then ascends 3 feet. How far below
the surface is he?
3. A croquet ball has a mass of
460 grams. Together, the mass of a
golf ball and a croquet ball is the same
as the mass of 11 golf balls. What is
the mass of one golf ball?
4. The temperature recorded at 5:00 A.M.
was 25°F. The temperature increased
by 2°F every hour for the next four
hours. What was the temperature at
the end of the four hours?
5. In a farmyard, there are 12 horses
and ducks altogether. If José counts
42 legs, how many horses and ducks
are there?
6. The Wiggins family spent a total of
$29.00 on tickets to go to a movie. If
adult tickets are $7.00 and children’s
tickets are $5.00, how many adult and
children’s tickets did they purchase if
there are 5 people in the family?
Grade 5
40
Chapter 6
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. At 3:00 A.M, the tide was 4 feet. By
9:00 A.M., the tide had risen 6 feet.
Andre calculates that the tide reached
10 feet at 9:00 A.M. Is his calculation
correct? Explain.
7–1
Name
Date
Skills Practice
Chapter Resources
Median and Mode
Find the median and mode of each set of data.
1. 1, 2, 0, 5, 8, 2, 9, 2, 7
2. 9, 4, 7, 9, 3, 10, 8, 6
3. 34, 17, 10, 23, 21, 15
4. 67, 67, 98, 49, 98, 89
5. 27, 31, 76, 59, 33, 48, 24, 58
6. 105, 126, 90, 50, 75, 90, 62, 112
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7. $1.50, $2.50, $1.50, $4.00, $5.00
8. 1.2, 1.5, 2.1, 1.7, 3.2, 2.4, 2.8, 1.3
9. 20, 12.5, 30, 15.4, 25, 18.6, 17.8
10. $3.35, $8.50, $3.35, $4.35, $8.25
11.
Student
Number of Pets
Grade 5
Ann
Ben
Cara
Fran
Ian
Mike
Kim
Lou
4
6
0
3
2
5
2
3
9
Chapter 7
Date
Skills Practice
Problem–Solving Investigation: Choose the Best Strategy
Solve.
1. Tim is building a wall with plastic bricks. Each row contains 10
bricks. The first row has 2 red bricks and 8 blue bricks. The second
row has 3 red bricks and 7 blue bricks. The third row has 4 red
bricks and 6 blue bricks. If the pattern continues, how many blue
bricks will there be in the sixth row of the wall?
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. Bob has cats and ducks as pets. Bob has twice as many cats as
ducks. He counts a total of 30 legs among all his cats and ducks.
How many cats and ducks does Bob have?
3. Michael and Dwight work together. Michael makes twice as much
money as Dwight does, and together they make $60,000 per year.
How much money does Dwight make?
4. Ben, Ray, Don, and Chris are going on a ski trip. The hotel where
they want to stay costs $100 per person each night. If they stay at
the hotel for four nights, what is the total cost?
5. Heidi just started a new job at a restaurant. On her first night, she
made $20 in tips. On the second night, she made $25, and on
the third night she made $30. If this pattern continues, how much
money will she make on the fifth night?
Grade 5
15
Chapter 7
Chapter Resources
7–2
Name
7–3
Name
Date
Skills Practice
Chapter Resources
Line Plots
The Johnson family kept a record of the length of telephone calls they
made in one weekend.
8
7
3
9
minutes
minutes
minutes
minutes
6
8
9
8
minutes
minutes
minutes
minutes
4
8
7
7
minutes
minutes
minutes
minutes
10 minutes
7 minutes
8 minutes
9 minutes
4
9
4
7
minutes
minutes
minutes
minutes
8 minutes
8 minutes
6 minutes
1. Make a line plot of the data.
Length of Phone Calls
3
4
5
6
7
8
9
10
Time in Minutes
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Use the data from your line plot for Exercises 2–5.
2. Find the median and mode of the data.
3. Write a few sentences describing the data in the line plot using the
median and the mode.
4. Find the range and any outliers of the data.
5. Write a few sentences describing the data in the line plot using the
range and outliers.
Grade 5
19
Chapter 7
7–4
Name
Date
Skills Practice
Frequency Tables
The table shows the names of several
famous artists.
Famous Artists
Matisse Monet
Manet Renoir
Dali
Miro
Tally
Grade 5
R
D
S
R
D
R
P
P
S
S
S
P
T
S
T
S
S
D
T
R
S
D
D
S
R = reading
D = drawing
P = photography
S = sports
T = watching TV
4. What is the mode of the data?
Frequency
24
Chapter 7
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Classmates’ Hobbies
3. Make a frequency table of the data.
Tally
Degas
Chagall
Frequency
Violet took a survey of her classmates’
hobbies. Her results appear in the
table.
Hobbies
Van Gogh Magritte
Da Vinci
Gauguin
2. Find the median, mode, and range of
the data. Identify any outliers.
1. Make a frequency table to show the
number of letters in each name.
Number of Letters
Cezanne Picasso
Rothko
Whistler
Date
Skills Practice
Scales and Intervals
The table shows the 25 highest
mountains in Texas.
Highest Mountains in Texas (ft)
8,378
6,781
8,631
7,748
6,717
7,835
8,508
6,814
8,085
6,580
7,031
8,749
7,550
6,521
6,725
7,730
6,894
8,615
6,432
6,350
8,368
6,860
6,398
7,825
6,650
Source: Texas State Library
1. Choose an appropriate scale and
interval size for a frequency table that
will represent the data. Then make a
frequency table.
25 Highest Mountains in Texas
Height (ft)
Tally
Frequency
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. Write a sentence or two to describe
how the data are distributed among
the intervals.
The table shows race results to the
nearest tenth for the school track team.
Track Team Race Times (min.)
10.3
11.7
10.1
12.8
10.7
11.9
9.5
7.3
9.7
10.8
12.1
13.6
9.3
9.1
14.5
3. Choose an appropriate scale and
interval size for a frequency table that
will represent the data. Then make a
frequency table.
Track Team Race Times
Time (min.)
4. Write a sentence or two to describe
how the data are distributed among
the intervals.
Grade 5
29
Tally
Frequency
Chapter 7
Chapter Resources
7–5
Name
7–6
Name
Date
Skills Practice
Bar Graphs
1. The table shows the times Ken and Pat
rode their bikes each day last week.
Make a double-bar graph of the data.
Day
Ken
Sunday
20
Monday
30
Tuesday
25
Wednesday
5
Thursday
20
Friday
15
Saturday
30
Pat
25
40
20
45
35
35
20
Baseball Playoff Scores
12
Hawks
2. What is the mode of the data?
10
8
Runs
3. Who won Game 4?
By how many runs?
Rockets
6
4
4. The team that wins 3
games wins the playoffs.
Who won the playoffs?
2
0
Game 1 Game 2 Game 3 Game 4 Game 5
Game
Grade 5
34
Chapter 7
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Use data from the graph at
right for Exercises 2–4.
Time Spent Riding a Bike (minutes)
7–7
Name
Date
Skills Practice
Chapter Resources
Line Graphs
The table shows Beth’s airplane trips from 2003–2008.
1. Make a line graph to display
the data in the table.
Beth’s Airplane Trips
Year
2003
Number of Trips
2
2004
2005
2006
2007
2008
3
7
7
5
6
Use the graph at the right for Exercises
2–4. It shows the Martin family vacations
from 2003—2008.
12
10
8
6
3. On a line graph, a line that rises shows
that a quantity is increasing. In which
years did the number of travel days
increase?
4
4. In which years did the number of travel
days decrease?
2
0
2003 2004 2005 2006 2007 2008
Year
Lemonade Sales
60
For Exercises 5—7 refer to the double line
graph. It shows Sue’s and Brett’s lemonade
sales.
5. Who sold more lemonade in nine days?
6. In all, how many glasses did Sue sale?
50
Number of Glasses
40
30
20
10
Sue
Grade 5
39
Day 9
Day 8
Day 7
Day 6
Day 5
Day 4
Day 3
Day 2
0
7. What was the difference in cups sold
between Sue and Brett?
Day 1
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. In which year(s) did they have the most
travel days?
Martin Family Vacation
Brett
Chapter 7
7–8
Name
Date
Skills Practice
Use an Appropriate Graph
Which type of graph would you use to display the data in each
table? Explain why. Then make the graph.
1. CDs owned by Patrick
Type of CD
Country
Rock
Rap
Blues
Pop
2. The number of laps completed by
students jogging around Lincoln Park
Number of CDs
3
10
8
6
2
Number of Laps Number of Students
1
4
2
3
3
5
4
2
3. Number of books read for
different ages
Time
1 P.M.
2 P.M.
3 P.M.
4 P.M.
Books Read
25
35
50
75
Temperature
64°F
68°F
70°F
66°F
Solve.
5. Write a problem in which you could use a graph to display the data. Share it
with others.
Grade 5
44
Chapter 7
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Age
8
9
10
11
4. Temperatures at different times
7–9
Name
Date
Skills Practice
Problem-Solving Strategy: Make a Graph
Solve by using a graph.
1. Renee surveyed her classmates to find out how many books they
had in their backpacks. What was the most frequent number of
Books in Backpacks
books found in a backpack?
Number of Books
3 2 2 0 1 3 4
2 2 2 3 1 4 2
4 3 1 3 1 3 3
0
1
2
3
4
5
Number of Books
2. In which years was there an increase in the mean math test scores
of Mrs. Sprankle’s fifth-grade class?
Math Test Scores
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Math Test Scores
Year
Mean Score
2000
86
2001
83
2002
88
2003
87
2004
85
2005
83
2006
86
3. The following table shows the kinds of movies favored by students
in fourth and fifth grades. What kind of movie is favored most by
students in both grades?
Favorite Movies
Movie Type
4th
5th
Graders
Graders
Comedy
17
19
Drama
5
7
Animation
11
8
Horror
7
10
Grade 5
50
Chapter 7
Skills Practice
Fractions and Division
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Represent each situation using a fraction. Then solve.
1. Mr. Janson has 3 jars of soup to divide
among 4 people. How much soup will
each person receive?
2. Andrew shares his suitcase with his
two brothers on vacation. How much
space in the suitcase will Andrew and
his brothers each have?
3. Two small pizzas are shared by three
people. How much pizza does each
person get?
4. One container of paint is used to paint
7 tables. How much paint did each
table use?
5. Five cupcakes are divided among 4
people. How many cupcakes does
each person get?
6. Four loaves of bread are divided
equally among three students. How
much bread will each student get?
Grade 5
9
Chapter 8
Chapter Resources
8–1
Name ____________________________ Date ________________
8–2
Name ____________________________ Date ________________
Skills Practice
Improper Fractions
Write each improper fraction as a mixed number.
5
2. _
3
19
3. _
3
3
4. _
2
17
5. _
4
31
6. _
5
16
7. _
5
4
8. _
3
13
9. _
9
11
10. _
3
49
11. _
8
8
12. _
5
44
13. _
9
12
14. _
11
38
15. _
7
20
16. _
7
41
17. _
8
10
18. _
7
19
19. _
5
7
20. _
3
29
21. _
9
17
23. _
6
9
24. _
2
45
25. _
8
68
26. _
7
12
27. _
5
22
28. _
3
49
29. _
6
28
30. _
3
22.
51
_
8
Grade 5
14
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
13
1. _
2
Chapter 8
8–3
Name ____________________________ Date ________________
Skills Practice
Problem-Solving Strategy
Solve. Use logical reasoning.
1. Julia can make 2 pieces of toast in 3 minutes. How long will it take
her to make 8 pieces of toast?
2. Jeff has saved $40.50. He wants to buy a new pair of shoes which
cost $35.75. The sales tax on these shoes is $2.50. How much
money will Jeff have left over after making this purchase?
3. In the school choir there are 3 more boys than girls. There are
13 boys and girls in the choir in all. How many boys are there in
the choir?
Country
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. The following chart shows some of the countries who earned the
most gold medals in the 2006 Winter Olympics. How many more
medals did Austria win than Estonia?
Number of Gold Medals
Germany
11
Austria
9
South Korea
6
Estonia
3
5. Louise, Jacqueline, and Martha ran a one-mile race. Louise finished
in 8.47 minutes, Jacqueline finished in 9.32 minutes, and Martha
finished in 8.34 minutes. How much time passed between Martha’s
finish and Jacqueline’s finish?
6. Shamera and Diana have played 14 games of checkers. Shamera
has won 2 more games than Diana. How many games has Diana
won?
Grade 5
20
Chapter 8
8–4
Name ____________________________ Date ________________
Skills Practice
Mixed Numbers
Write each mixed number as an improper fraction.
1
1. 3 _
2
3
2. 5 _
4
7
3. 6 _
8
5
4. 5 _
12
1
5. 4 _
6
2
6. 6 _
3
2
7. 12 _
3
23
8. 10 _
100
1
9. 9 _
4
1
11. 25 _
4
1
12. 22 _
2
4
13. 6 _
5
3
14. 4 _
10
1
15. 6 _
100
5
16. 7_
8
3
17. 6 _
8
9
18. 3 _
100
5
19. 5_
6
3
20. 9 _
17
1
21. 25 _
3
2
22. 5_
9
2
23. 12 _
3
3
24. 5 _
7
4
25. 6 _
9
1
26. 10 _
18
5
27. 5 _
12
2
28. 6 _
13
4
29. 25 _
5
5
30. 20 _
6
Solve.
1
31. Tina spent 3_ hours practicing the
3
piano. Write this quantity as an
improper fraction.
Grade 5
1
32. Suppose you have 2_ oranges. Write
4
this quantity as an improper fraction.
24
Chapter 8
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2
10. 8 _
5
Date
Skills Practice
Fractions on a Number Line
with < or > to make a
Use the number line for Exercises 1–6. Replace each
true statement.
1
7
0
3
7
4
7
5
7
1.
1
_
3
_
2.
6
_
4.
9
_
2
_
5.
11
_
7
7
7
7
7.
2
_
10.
9
_
13.
9
_
4
10
5
7
6
7
7
7
8
7
9
7
10 11 12 13 14 15
7 7 7
7 7 7
4
_
7
1
2_
7
7
1
3. 1 _
7
14
_
2
6. 1 _
7
8
_
7
7
with < or > to make a true statement.
Replace each
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2
7
3
_
4
2
_
10
3
1_
5
1
8. 1 _
9
8
_
9.
5
_
2
11. 1 _
8
11
_
12.
14
_
3
2_
7
7
_
6
_
15.
10
_
1
2_
4
14.
9
8
11
11
2
_
6
6
7
4
Write the fraction or mixed number that is represented by each point.
P
0
Q
R
S
1
T
U
2
3
16. P
17. Q
18. R
19. S
20. T
21. U
Solve.
3
1
22. Amelia’s bookshelf is _ full of books and _ full of magazines.
5
5
Does her bookshelf have more books or magazines? Explain.
Grade 5
29
Chapter 8
Chapter Resources
8-5
Name
8–6
Name
Date
Skills Practice
Round Fractions
Round each number to 0,
_1 or 1.
2
1.
3
_
2.
12
_
3.
9
_
4.
3
_
5.
2
_
6.
2
_
7.
1
_
8.
3
_
9.
7
_
10.
1
_
11.
12
_
12.
2
_
13.
1
_
14.
11
_
15.
5
_
16.
2
_
17.
1
_
18.
4
_
19.
2
_
20.
1
_
21.
8
_
12
4
2
8
4
16
9
8
15
12
3
5
18
3
8
9
6
5
9
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8
13
Solve.
22. Mrs. Jones is putting up blinds to fit in a window opening that is
7
7
_
yard wide. Should she round _ up or down when deciding on
8
8
the size of blinds to purchase?
1
23. Marvin is mailing a copy of a document that is 12 _ inches long
8
1
and 10 _ inches wide. Will the document fit in an envelope that is
2
1
12 inches long and 10 _ inches wide or in an envelope that is
2
1
12 _ inches long and 11 inches wide?
2
Grade 5
34
Chapter 8
8–7
Name
Date
Skills Practice
Problem-Solving Investigation: Choose the Best Strategy
Use any strategy shown below to solve.
• Guess and check
• Work backward
• Solve a simpler problem
• Make a table
• Use logical reasoning
• Act it out
1. In how many ways can 5 people stand in line if one of the people
always has to be first in line?
2. The teacher told the class of 30 students that
1
_
of them scored
2
1
above an 80 on their math test. An additional _ of them scored at
3
least a 70. How many of them scored below 70?
3. Alicia bought a CD player for $10 less than the regular price. If she
paid $58 for the CD player, what was the regular price?
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1
4. Miguel bought boxes of chocolates. The first box weighed 4 _
4
3
1
_
_
pounds, the second, 2 , and the third, 1 . What is the total
4
3
amount of chocolate that Miguel bought?
5
5. After Miguel shared the chocolate with his friends, he had 3 _
8
3
_
pounds left. Then, he gave 2 pounds to his mother. Now, how
4
much does he have?
6. The first
3
1
_
mile of a _ -mile path through a rose garden is paved
5
4
with bricks. How much of the path is not paved with bricks?
Grade 5
40
Chapter 8
9–1
Name
Date
Skills Practice
Chapter Resources
Common Factors
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Find the GCF of each set of numbers.
1. 10 and 15
2. 6 and 24
3. 16 and 36
4. 24 and 30
5. 9 and 21
6. 12 and 40
7. 8 and 28
8. 18 and 27
9. 12 and 60
10. 14 and 18
11. 20 and 30
12. 24 and 45
13. 27 and 30
14. 10 and 22
15. 12 and 36
16. 11 and 15
17. 18 and 45
18. 21 and 27
19. 13 and 25
20. 8 and 48
21. 16 and 18
22. 24 and 36
23. 4, 12, and 30
24. 12, 18, and 36
25. 9, 16, and 25
26. 9, 15, and 21
27. 12, 15, and 21
28. 9, 36, and 45
29. 3, 9, and 31
30. 15, 30, and 50
31. 16, 24, and 30
32. 30, 50, and 100
Solve.
34. Rosa found 8 different wildflowers
and 20 different leaves on her hike.
She plans to display them in 7 equal
rows on a poster. What is the greatest
number of flowers or leaves she can
put in each row?
33. Thirty people at the nature center
signed up for hiking, and 18 signed up
for bird watching. They will be divided
into smaller groups. What is the
greatest number of people that can be
in each group and have all groups the
same size?
Grade 5
9
Chapter 9
9–2
Name
Date
Skills Practice
Prime and Composite Numbers
Tell whether the number represented by each model is prime or
composite.
1. 6
2. 12
3. 7
Tell whether each number is prime or composite.
5. 45
6. 18
7. 23
8. 39
9. 55
10. 28
11. 79
12. 62
Problem Solving.
Solve.
13. There are 24 students in Mrs.
Blackwell’s class. The number of boys
and the number of girls are both prime
numbers. There are 2 more boys than
girls. How many boys and how many
girls are in the class?
Grade 5
14. There are 27 students in Mr.
Rodriguez’s class. The number of
boys and the number of girls are both
composite numbers. There are 3 more
girls than boys. How many girls and
how many boys are in the class?
14
Chapter 9
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. 64
Name
9–3
Date
Skills Practice
Chapter Resources
Equivalent Fractions
Find two fractions that are equivalent to each fraction.
1.
1
_
2.
1
_
3.
2
_
4.
5
_
5.
7
_
6.
2
_
7.
8
_
8.
3
_
9.
4
_
10.
4
_
2
5
8
10
12
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Algebra Find the number for
4
6
3
8
16
that makes the fractions equivalent.
11.
1
_
=_
12.
3
_
=_
13.
7
_
=_
14.
8
_
=_
15.
10
_
=_
16.
4
_
=_
17.
3
_
=_
18.
6
2
_
=_
19.
12
_
=_
4
12
5
12
3
20
5
12
10
6
3
10
10
16
20
5
4
Problem Solving.
Solve.
23. Nina used 24 tiles to make a design.
Six of the tiles were blue. Write two
equivalent fractions that name the part
of the tiles that were blue.
Grade 5
24. Chris walks
3
_
mile each day to school.
8
1
Anna walks _ mile. Do they walk the
2
same distance to school? Explain.
19
Chapter 9
9–4
Name
Date
Skills Practice
Simplest Form
Write each fraction in simplest form.
1.
4.
7.
10.
13.
16.
4
_
28
30
_
35
9
_
24
14
_
21
8
_
14
24
_
40
2.
5.
8.
11.
14.
17.
15
_
3.
20
3
_
30
14
_
42
16
_
18
14
_
35
12
_
30
4.
9.
12.
15.
18.
6
_
21
12
_
14
20
_
25
4
_
36
10
_
12
4
_
32
Write each fraction in simplest form. If the fraction is already in
simplest form, write simplified.
16
_
20
2
22. _
5
40
25. _
48
15
28. _
36
20.
1
_
21.
2
3
23. _
7
12
26. _
18
2
29. _
3
3
_
12
28
24. _
32
5
27. _
8
3
30. _
24
Solve.
31. Of the 27 students in Jarrod’s class, 18
receive an allowance each week. What
fraction of the students, in simplest
form, receive an allowance?
Grade 5
32. Of the 18 students who receive an
allowance, 14 do chores around the
house. What fraction of these students,
in simplest form, do chores around the
house?
24
Chapter 9
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
19.
9–5
Name
Date
Skills Practice
Chapter Resources
Decimals and Fractions
Write each decimal as a fraction in simplest form.
1. 0.3
2. 0.49
3. 0.7
4. 0.50
5. 0.94
6. 0.80
7. 0.72
8. 0.2
9. 0.55
10. 0.1
11. 0.25
12. 0.03
13. 0.77
14. 0.6
15. 0.26
16. 0.99
17. 0.36
18. 0.75
19. 0.70
20. 0.4
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write each decimal as a mixed number in simplest form.
21. 8.9
22. 12.1
23. 14.5
24. 17.03
25. 9.35
26. 42.96
27. 7.425
28. 50.60
29. 8.43
30. 3.25
31. 2.25
32. 1.33
33. 4.10
34. 7.75
35. 8.60
36. 16.03
Solve.
37. The largest butterfly in the world is
found in Papua, New Guinea. The
female of the species weighs about
0.9 ounce. Use a fraction to write the
female’s weight.
Grade 5
38. The shortest recorded fish is the
dwarf goby found in the Indo-Pacific.
The female of this species is about
thirty-five hundredths inch long. Use a
decimal to write the female’s length.
29
Chapter 9
Date
Skills Practice
Problem Solving Strategy: Look for a Pattern
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve. Use the look for a pattern strategy.
1. Martina is designing chains. The
diagram shows the number of
rings she uses in each chain. If she
continues the pattern, how many rings
will be in the next chain?
2. A sculptor is using a pattern of glass
cubes to create a sculpture with 5
sections. The first section has 4 cubes,
the second section has 8 cubes, and
the third section has 16 cubes. If the
pattern continues, how many cubes
are in the fifth section?
3. Mika is making a pattern of circles.
The smallest circle has a diameter of
8 centimeters. The next circle has a
diameter of 12 centimeters and the
circle after that has a diameter of 16
centimeters. What is the diameter of
the sixth circle?
4. The bottom layer of a pyramid has 150
blocks. The layer above the bottom has
120 blocks. The third layer from the
bottom has 90 blocks. If the pattern
continues, how many blocks will be in
the next two layers?
5. In a set of bowls, the diameters of
the bowls increase in a pattern. The
smallest bowl has a diameter of 15
centimeters, the next bowl has a
diameter of 21 centimeters. If the
largest bowl has a diameter of 45
centimeters, what are the diameters of
the other three bowls?
6. The price of apples at a farm market is
shown in the table. How much will 12
apples cost?
Grade 5
Number of
Apples
3
6
9
12
35
Cost
($)
$1.50
$3.00
$4.50
Chapter 9
Chapter Resources
9–6
Name
9–7
Name
Date
Skills Practice
Chapter Resources
Multiples
Find the least common multiple (LCM) of the numbers.
1. 5 and 15
2. 2 and 9
3. 2 and 11
4. 6 and 9
5. 4 and 5
6. 8 and 12
7. 4 and 8
8. 10 and 25
9. 3 and 4
10. 2 and 3
11. 8 and 9
12. 4 and 10
13. 2, 4, and 16
14. 3, 5, and 6
15. 3, 6, and 8
Identify the first three common multiples of each set of numbers.
16. 2, 5
17. 1, 6
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
18. 2, 3, 4
19. 7, 14
Solve.
20. José and Sara are walking around the
track at the same time. José walks
one lap every 8 minutes. Sara walks a
lap every 6 minutes. What is the least
amount of time they would both have
to walk for them to cross the starting
point together?
Grade 5
21. Pamela and David walk on the same
track. It takes Pamela 9 minutes and
David 6 minutes to walk one lap. If
they start walking at the same time,
how many laps will each have walked
when they cross the starting point
together for the first time?
39
Chapter 9
Date
Skills Practice
Problem-Solving Investigation: Choose the Best Strategy
Choose any strategy shown below to solve each problem.
• Guess and check.
• Act it out.
• Make a table.
1. In a farmyard, there are 10 cows and chickens altogether. If Sondra
counts 26 total legs, how many cows and chickens are there?
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. Maria is reading a book. Each day, she reads three more pages than
the day before. If she read 22 pages the first day, how many pages
will she have read altogether after the sixth day?
3. Jerry’s team played 12 games, and during that time he made 42
baskets. If he played in 2 games out of every 4 that the team played
and he made an equal number of baskets each of these games,
how many baskets did he make each game?
4. Patty’s goal was to make 40 bracelets. She made 5 bracelets the
first week, 5 bracelets the second week, and 10 bracelets the third
week. What fraction of her goal did she make?
5. At the end of basketball season, the player with the most points
wins a basketball. Davina scored one point in the first game and
one more each game than she had in the previous game for 5
games. Sally got 3 points each game for 4 games. Who had the
most total points?
Grade 5
45
Chapter 9
Chapter Resources
9–8
Name
9–9
Name
Date
Skills Practice
Chapter Resources
Compare Fractions
Compare each pair of fractions using the LCD.
1.
2 _
1
_
,
2.
1
1 _
_
,
3.
3 _
1
_
,
4.
7
2 _
_
,
5.
5
5 _
_
,
6.
5 _
7
_
,
7.
2 _
1
_
,
8.
1 _
2
_
,
9.
1
7 _
_
,
10.
3 _
1
_
,
1
2 _
_
,
12.
3
3 _
_
,
11.
5 10
8 12
9 8
5 4
12 10
9 2
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Replace each
13.
3
_
7
_
4
12
16.
1
_
7
_
2
10
19.
7
_
8
_
8
9
22.
4
_
17
_
5
20
25.
1
_
1
_
5
4
9 12
5 8
8 10
5 15
4 8
15 10
with >, <, or = to make a true sentence.
14.
2
_
3
_
5
4
17.
15
_
3
_
16
8
20.
2
_
1
_
10
5
23.
1
_
2
_
8
5
26.
5
_
3
_
8
5
15.
1
_
1
_
6
3
18.
3
_
5
_
8
6
21.
11
_
5
_
12
8
24.
2
_
4
_
3
6
27.
1
_
4
_
6
18
Solve.
28. Visitors to an art museum were asked to name a favorite type of art. Pottery was
9
2
named by _ of the visitors, painting was named by _ , and sculpture was named
5
40
3
by _. What was the favorite type of art of most visitors?
8
Grade 5
49
Chapter 9
Name ____________________________ Date ________________
10–1
Skills Practice
Chapter Resources
Add Like Fractions
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Add. Write each in simplest form.
1.
7
1
_
+_=
2.
13
7
_
+_=
3.
4
1
_
+_=
4.
5
7
_
+_=
5.
3
4
_
+_=
6.
5
5
_
+_=
7.
7
2
_
+_=
8.
9
3
_
+_=
9.
3
1
_
+_=
10
10
12
12
15
15
16
5
20
16
5
20
5
5
6
6
8
8
10.
3
1
_
+_=
11.
2
1
_
+_=
12.
5
1
_
+_=
13.
7
3
_
+_=
14.
3
9
_
+_=
15.
7
7
_
+_=
16.
7
11
_
+_=
17.
19
5
_
+_=
18.
11
7
_
+_=
19.
9
7
_
+_=
20.
4
3
_
+_=
21.
7
4
_
+_=
8
8
16
16
12
12
16
16
3
10
20
5
3
10
20
5
6
6
8
8
20
20
9
9
with >, <, or = to make a true sentence.
Replace each
22.
5
7
_
+_
3
3
_
+_
23.
9
7
_
+_
24.
2
2
_
+_
5
7
_
+_
25.
3
3
_
+_
9
5
_
+_
26.
3
3
_
+ _
27.
5
7
_
+_
13
11
_
+_
8
3
5
Grade 5
8
3
5
4
12
4
12
7
7
_
+ _
10
10
9
10
8
8
10
8
8
3
4
_
+_
5
16
16
5
16
16
Chapter 10
Name ____________________________ Date ________________
10–2
Skills Practice
Subtract Like Fractions
Subtract. Write each difference in simplest form.
1.
7
1
_
-_=
2.
13
7
_
-_=
3.
4
1
_
-_=
4.
5
7
_
-_=
5.
3
4
_
-_=
6.
5
4
_
-_=
7.
7
2
_
-_=
8.
9
3
_
-_=
9.
3
1
_
-_=
10.
3
1
_
-_=
11.
2
1
_
-_=
12.
5
1
_
-_=
13.
7
3
_
-_=
14.
9
3
_
-_=
15.
7
7
_
-_=
11
7 =
16. _ - _
12
12
17.
19
5
_
-_=
18.
11
7
_
-_=
19.
9
_
20.
4
3
_
-_=
10
5
5
15
8
3
10
5
5
15
8
3
16
16
8
20
20
7
-_=
16
16
16
12
12
6
6
20
20
8
8
6
6
10
10
20
20
5
5
with >, <, or = to make a true sentence.
Replace each
21.
5
7
_
-_
3
3
_
-_
22.
7
9
_
-_
23.
1
2
_
-_
7
5
_
-_
24.
3
3
_
-_
5
9
_
-_
25.
3
5
_
- _
10
7
_
- _
10
10
26.
7
5
_
-_
13
11
_
-_
8
3
5
Grade 5
8
3
5
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8
16
4
12
4
12
14
10
8
8
4
3
_
-_
5
10
8
8
16
16
5
16
16
Chapter 10
10–3
Name ____________________________ Date ________________
Skills Practice
Chapter Resources
Add Unlike Fractions
Add. Write your answer in simplest form.
1.
5.
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9.
1
_
2
1
_
+
5
9
_
10
7
_
+
10
3
_
4
2
_
+
5
2.
6.
10.
2
_
5
7
_
+
10
3.
7
_
12
1
+_
3
7.
7
_
12
3
+_
4
11.
5
_
8
3
_
+
16
9
_
10
2
+_
5
2
_
3
3
_
+
8
4.
8.
12.
3
_
5
3
_
+
20
3
_
16
3
+_
8
9
_
20
3
+_
5
3
7
13. _ + _ =
8
16
5
7
14. _ + _ =
6
12
15
5
15. _ + _ =
8
16
3
17
16. _ + _ =
4
20
1
4
17. _ + _ =
4
5
1
1
18. _ + _ =
5
2
5
2
19. _ + _ =
5
8
7
1
20. _ + _ =
2
10
5
5
21. _ + _ =
6
8
3
5
22. _ + _ =
8
10
3
1
23. _ + _ =
5
4
5
7
24. _ + _ =
6
9
9
7
25. _ + _ =
20
10
5
3
26. _ + _ =
5
6
5
35
27. _ + _ =
8
12
Problem Solving
Solve.
3
28. After school, Michael walks _ mile to
3 5
the park and then walks _ mile to his
4
house. How far does Michael walk
from school to his house?
Grade 5
29. When Rachel walks to school on the
7
sidewalk, she walks _ mile. When
10
she takes the shortcut across the field,
1
she walks _ mile less. How long is the
4
shorter route?
19
Chapter 10
10–4
Name ____________________________ Date ________________
Skills Practice
Subtract Unlike Fractions
Write the subtraction sentence shown by each model.
Write the difference in simplest form.
1.
1
_
5
1
_
5
1
_
5
2.
1 _
1 _
1 _
1 _
1 _
1
_
1
_
6
10 10 10 10 10 10
4.
1
_
4
1 _
1 _
1 _
1 _
1 _
1
_
10 10 10 10 10 10
1
_
3
5.
1
_
3
1
_
6
1
_
8
1
_
6
1
_
8
12 12 12 12 12 12 12 12 12
6.
1 _
1 _
1 _
1 _
1 _
1 _
1 _
1 _
1
_
12 12 12 12 12 12 12 12 12
1
_
4
1 _
1 _
1 _
1 _
1 _
1 _
1 _
1 _
1
_
1
_
6
1
_
8
1
_
4
1
_
4
3.
1
_
6
1
_
6
1
_
6
1
_
6
1
_
6
1
_
6
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24
Subtract. Write your answer in simplest form.
9
2 =
9. _ - _
10
5
8
1 =
10. _ - _
5
4
11
3 =
11. _ - _
20
10
11
1 =
12. _ - _
12
3
7
1 =
13. _ - _
10
2
3
2 =
14. _ - _
4
3
5
3 =
15. _ - _
6
4
3
3 =
16. _ - _
4
5
11
1 =
17. _ - _
12
4
4
1 =
18. _ - _
5
2
Problem Solving
Solve.
19. The distance around a lily pound is
7
_
mile. Rocks have been placed
10 _
1
for mile along the pond’s edge. How
4
much of the edge does not have rocks?
Grade 5
20. The first _ mile of a _ mile path
5
4
through a rose garden is paved with
bricks. How much of the path is not
paved with bricks?
24
1
3
Chapter 10
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1
1 =
8. _ - _
2
3
7
1
7. _ - _ =
4
12
10–5
Name ____________________________ Date ________________
Skills Practice
Problem-Solving Strategy: Determine Reasonable Answers
Solve. Determine which answer is reasonable.
1. Ms. Montoya makes 2_34_ pounds of goat cheese in the morning. In
the afternoon, she makes 1_14_ pounds of goat cheese. Is 3 pounds,
4 pounds, or 5 pounds a more reasonable estimate for how much
goat cheese Ms. Montoya makes in one day?
2. The Wilsons decide to churn butter for a family project. The boys in
the family make 2.5 pounds of butter. The girls in the family make
4.7 pounds of butter. Which is a more reasonable estimate for how
much more butter the girls made than the boys: 2 pounds,
3 pounds, or 4 pounds?
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. Clara picks 5.75 bushels of apples. Franz picks 3.25 bushels of apples.
Is 2 bushels, 3 bushels, or 4 bushels a more reasonable estimate for
how many more bushels Clara picked than Franz?
4. On Monday, Tina makes 4.7 pounds of raisins from grapes. On
Tuesday, she makes 3.8 pounds of raisins. Which is a more
reasonable estimate for about how many pounds of raisins she
made in all: 7 pounds, 8 pounds, or 9 pounds?
5. Miguel picked 3.68 pounds of grapes last week. This week, he
picks 2.27 pounds of grapes. Is 5 pounds, 6 pounds, or 7 pounds
a more reasonable estimate for how many pounds Miguel picked
altogether?
Grade 5
30
Chapter 10
10–6
Name ____________________________ Date ________________
Skills Practice
Estimate Sums and Differences
Round each mixed number to the nearest whole number.
3
1. 7 _
4
9
5. 2 _
16
1
2. 4 _
6
4
6. 9 _
5
4
3. 8 _
10
7
7. 1 _
8
4
4. 3 _
5
5
8. 5 _
12
5
2
10. 8 _ - 3 _
3
6
1
7
11. 5 _ - 1 _
8
8
7
4
12. 9 _ + 3 _
5
10
3
1
13. 6 _ + 7 _
4
8
3
1
14. 14 _ - 9 _
5
5
5
13
15. 18 _ - 9_
16
16
5
11
16. 6 _ + 4 _
12
12
7
1
17. 7 _ + 7 _
3
12
3
7
18. 15_ - 7_
8
16
2
4
19. 9 _ + 6 _
5
3
11
1
20. 6 _ - 6 _
5
12
2
11
21. 8 _ + 8 _
5
16
7
1
22. 17_ - 9_
3
10
3
1
23. 7 _ + 9 _
3
8
7
1
24. 30 _ + 30 _
12
12
7
4
25. 58 _ - 29 _
5
8
5
1
26. 50 _ - 30 _
3
16
Solve.
27. Beth walks 10 _ miles in one week. She walks 2 _ fewer miles the following week.
4
8
About how many miles does she walk the second week?
7
1
28. Jon wants to walk at least 8 miles by the end of the week. He walks 5 _ miles by
4
5
Thursday. If he walks another 2 _ miles on Friday, will he meet his goal? Explain.
3
8
Grade 5
34
Chapter 10
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Estimate.
7
1
9. 3 _ + 2 _
6
8
Date
Skills Practice
Add Mixed Numbers
Add. Write each sum in simplest form.
1.
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6.
8
5_
12
9
+ 3_
12
9
5_
24
22
+ 6_
24
7
2. 12 _
8
2
+ 4_
8
7.
1
5_
5
5
_
+2
15
3.
8.
5
13 _
10
6
+ 4_
10
4
9_
8
1
_
+8
2
4.
9.
8
21 _
24
7
+ 5_
24
2
4_
12
3
+ 11 _
6
5.
10.
5
8_
10
8
+ 6_
10
9
7_
15
1
+ 1_
5
3
4
11. 4 _ + 5 _ =
10
10
7
4
12. 3 _ + 2 _ =
8
8
3
2
13. 5 _ + 3 _ =
12
12
3
2
14. 6 _ + 2 _ =
4
4
1
2
15. 1 _ + 3 _ =
12
12
3
4
16. 9 _ + 10 _ =
10
10
4
11
17. 7 _ + 5 _ =
12
12
7
18. 11_ + 4 =
10
8
9
19. 2 _ + 4 _ =
12
12
6
7
20. 7 _ + 2 _ =
8
8
3
5
21. 4 _ + 3 _ =
6
6
5
4
22. 7 _ + 1 _ =
6
6
15
1
23. 2 _ + 4 _ =
4
20
3
4
24. 5 _ + 7 _ =
8
16
5
3
25. 14 _ + 8 _ =
16
8
10
6
26. 15 _ + 12 _ =
8
16
15
2
27. 9 _ + 4 _ =
12
18
1
2
28. 12 _ + 6 _ =
3
6
Solve.
2
29. A cave is 5_ miles west of a waterfall.
4
1
A group of hikers is 2_ miles east of
4
the waterfall. How far is the group of
hikers from the cave?
Grade 5
30. A mark on the side of a pier shows
7
that the water is 4 _ ft deep. When
8
the tide is high, the depth increases by
3
2 _ ft. What is the depth of the water
4
when the tide is high?
39
Chapter 10
Chapter Resources
10–7
Name
10–8
Name
Date
Skills Practice
Subtract Mixed Numbers
Subtract. Write each difference in simplest form.
1.
6.
11
10 _
16
14
_
- 3
16
1
7_
2
3
_
-3
6
2.
7.
5
8_
8
3
_
-2
8
3
2_
4
1
_
-1
8
3.
8.
3
9_
5
2
_
-3
5
2
4_
16
1
- 2_
16
4.
9.
6
5_
8
1
_
-2
4
2
9_
3
1
_
-3
3
5.
10.
3
8_
5
2
_
-3
5
4
2_
5
4
_
-1
10
7
7
12. 6 _ - 2 _ =
8
8
7
1
13. 27 _ - 13 _ =
12
12
8
1
14. 5 _ - 1 _ =
4
20
2
1
15. 10 _ - 7 _ =
3
3
1
1
16. 7 _ - 2 _ =
3
9
3
2
17. 8 _ - 1 _ =
5
5
9
1
18. 10 _ - 2 _ =
5
10
3
1
19. 12 _ - 6 _ =
10
10
9
9
20. 5 _ - 3 _ =
12
12
5
1
21. 15 _ - 7 _ =
8
8
6
5
22. 11 _ - 6 _ =
8
8
Solve.
1
23. Anna has 3 _ yd of fabric. She plans to
2
1
use 2 _ yd for curtains. Does she have
4
enough left to make 2 pillows that
1
each use 1_ yd of fabric? Explain.
2
Grade 5
24. Paula has 2 yd of elastic. One project
3
needs a _ -yd piece. Does she have
4
enough for another project that needs
1
1 _ yd? Explain.
3
44
Chapter 10
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7
1
11. 15 _ - 8 _ =
2
12
10–9
Name
Date
Skills Practice
Problem-Solving Investigation: Choose the Best Strategy
Use any strategy to solve each problem.
2. Fifty five families that own pets were
asked what type of pets they own. Of
the families surveyed, 24 have dogs,
14 have cats, and 5 have both dogs
and cats. How many have neither a
dog nor cat?
1. Describe the pattern below. Then find
the missing number.
10, 20, 30,
, 50
4. Six students are sitting at a lunch table.
Two more students arrive, and at the
same time, three students leave. Then,
four students leave, and two more
arrive. How many students are at the
table now?
5. The sum of two whole numbers
between 20 and 40 is 58. The
difference of the two numbers is 12.
What are the two numbers?
6. Ramon has $3.50. He buys two pens
that cost $0.75 each and a pencil that
costs $0.40. How much money does
Ramon have left?
Grade 5
50
Chapter 10
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. A designer is making a tile mosaic.
The first row of the mosaic has 1 red
tile in the center. If the designer
increases the number of red tiles in
the center of each row by 4, how
many red tiles will be in the center
of the fifth row?
10–10
Name
Date
Skills Practice
Subtraction with Renaming
Subtract. Write each difference in simplest form.
6
1. 10 _
16
11
- 3_
16
5.
2.
1
8_
3
4
_
-3
6
6.
1
8_
3
2
_
-2
3
3.
5
7_
9
8
_
-3
9
7.
2
9_
5
4
_
-3
5
4.
1
2_
4
3
_
- 1
4
8.
3
5_
16
1
- 2_
2
1
4_
4
5
_
-2
8
2
4
9. 5 _ - 1 _ =
5
5
1
2
10. 10 _ - 7 _ =
3
3
3
1
11. 7 _ - 2 _=
4
4
5
2
12. 8 _ - 1 _ =
6
6
5
1
13. 10 _ - 2 _ =
3
9
6
2
14. 12 _ - 6 _ =
7
7
5
7
15. 5 _ - 3 _ =
6
12
5
1
16. 15 _ - 7 _ =
8
8
1
1
17. 11 _ - 6 _ =
4
2
2
18. 6 _ 5
1
20. 10 _ 3
3
_ = 1_
5
2
_ = 3_
3
3
19. 15 _ +
12
5
21. 6 _ 9
8
_ = 6_
12
6
_ = 3_
9
Solve.
1
22. Anna has 3 _ yd of fabric. She uses
4
3
2 _ yd for curtains. How much fabric
4
is left over?
3
23. Paula has 2 _ yard of elastic. One
6
4
project needs a 1 _ yard piece. Will she
6
have enough elastic to make another
project that uses the same amount?
Explain.
Grade 5
54
Chapter 10
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Find each missing number.
Date
Skills Practice
Units of Length
0
1
2
3
5
4
6
inches
Measure the length of the pencil to the nearest:
1.
inch
2.
half inch
3.
quarter inch
eighth inch
4.
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Choose an appropriate unit to measure the length of each. Write
inch, foot, yard, or mile.
5. distance from Boston to Dallas
6. height of a giraffe
7. length of an aircraft carrier
8. width of a computer diskette
Complete.
9. 900 in. =
12. 1,218 ft =
yd
yd
15. 1,332 in. =
yd
10. 46 yd =
ft
11. 948 in. =
13. 19 yd =
in.
14. 62 ft =
16. 792 ft =
yd
17. 127 ft =
18. 153 in. =
yd
19. 26 ft =
20. 113 in. =
ft
in.
21. 263 in. =
22. 519 in. =
ft
in.
23. 178 ft =
in.
yd
yd
yd
ft
in.
in.
ft
in.
ft.
Solve.
1
24. A piece of red ribbon is 4 _ ft long.
2
A piece of blue ribbon is 1 yd long.
How many feet longer is the piece
of red ribbon than the piece of blue
ribbon? How many inches longer?
Grade 5
25. A bookcase is 6 ft wide and a table is
30 in. wide. Will both fit along a wall
that is 3 yd long? Why or why not?
9
Chapter 11
Chapter Resources
11–1
Name
Date
Skills Practice
Problem-Solving Strategy: Draw a Diagram
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3
1. Michael ate _ of a pizza. Kenneth
8
1
ate _ of a pizza that was the exact
2
same size as Michael’s pizza. Who ate
more pizza?
2. Dominic’s house, his school, and the
park are on the same road. He lives
1
1
2 _ miles from the school, which is _
2
2
mile farther from his house than the
park. How far is it from Dominic’s
house to the park?
3. Mrs. Pintos is planting flowers around
the outside edge of a square garden.
There will be 10 plants on each
side of the garden. What is the least
number of flowers she needs to
plant?
4. Measurement A carpenter has a
piece of wood 12 feet long. After he
5
cuts the wood into pieces, 3 _ feet
8
are left. How much of the wood does
the carpenter use?
5. Five students are lined up in the
cafeteria. Beth is first in line. Jeff is
2 places behind Ernesto. Leah is
ahead of Peter, who is fifth in line.
Who is third in line?
6. For lunch, the corner deli has a
special where they sell a sandwich
and drink combo for $4.95.
Sandwiches
Ham
Turkey
Roast Beef
Veggie
BLT
Drinks
Soda
Milk
Juice
How many different sandwich and
drink combos are available at the deli?
Grade 5
15
Chapter 11
Chapter Resources
11–2
Name
11–3
Name
Date
Skills Practice
Chapter Resources
Units of Weight
Choose an appropriate unit to measure the weight of each.
Write ounce, pound, or ton.
1. bowling ball
2. compact disc
3. ocean liner
Complete.
4. 5 lb =
oz
7. 400 oz =
lb
10. 42 oz =
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
oz
6. 4
8. 64 oz =
lb
9. 8,000 lb =
lb
oz
T
lb 13. 89 oz =
14. 6,500 lb =
T
lb 15. 115 oz =
16. 6 lb
19. 7,000 lb
22. 15 lb
T
T
lb
lb
oz
lb
oz
with >, <, or = to make a true sentence.
100 oz
17. 5 lb
50 oz
18. 1 T
2,000 oz
6,000 lb
3T
20. 98 oz
8 lb
21. 3 T
300 oz
23. 55 oz
3 lb 10 oz
24. 130 lb
1,920 oz
26. Mr. Hill’s truck weighs 1 _12_ tons. His car
weighs 1,600 pounds. Which vehicle
weighs more? How much more?
25. Alfonso mails a package that weighs
9 pounds. How many ounces is the
package?
Grade 5
lb
2
11. 2,450 lb =
12. 3,500 lb =
Replace each
_1 T =
5. 12 lb =
19
Chapter 11
11–4
Name
Date
Skills Practice
Units of Capacity
Complete.
1. 38 pt =
4. 4 c =
qt
fl oz
pt
7. 48 fl oz =
10. 12 qt =
13. 3 c =
16. 21 fl oz =
gal
fl oz
2. 3 qt =
pt
5. 15 pt =
c
1
6. 5 _ qt =
2
8. 36 qt =
gal
9. 4 qt =
11. 40 fl oz =
c
14. 6 gal =
c
3. 9 c =
qt
fl oz
17. 70 fl oz =
qt
19. 34 pt =
15. 72 fl oz =
c
qt
with >, < or = to make a true sentence.
129 pt
gal
21. 8 pt 1 c
2 gal
22. 50 fl oz
24. 60 fl oz
10 c
25. 65 gal
fl oz
qt
1
1_ qt
2
256 qt
Solve.
26. Robert needs 3 pints of milk to make a
casserole. He has 5 cups of milk. How
many more cups of milk does Robert
need?
Grade 5
27. Shannon combines 3 quarts of
cranberry juice with 3 pints of apple
juice. Does Shannon now have at least
one gallon of cranberry juice? Why or
why not?
24
Chapter 11
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Replace each
23. 63 c
fl oz
pt
gal
4 gal 2 pt
pt
12. 64 fl oz =
18. 26 qt =
20. 20 qt
fl oz
11–5
Name
Date
Skills Practice
Chapter Resources
Units of Time
Complete.
1. 9 min =
3. 90 mo =
y
5. 12 h =
min
7. 7 years =
9. 58 h =
11. 6 d 9 h =
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. 96 h =
s
mo
mo
d
d
4. 15 wk =
d
6. 730 d =
y
8. 350 s =
min
10. 72 mo =
h
12. 60 d =
h
s
y
wk
d
13. A non-stop flight from Boston,
Massachusetts, to Chicago, Illinois,
takes 2 hours and 50 minutes. What is
this time in minutes?
14. Germaine entered a walk for charity.
He completed the walk in 48 minutes
and 35 seconds. What is this time in
seconds?
15. It took the Johnson family 2 days and
13 hours to drive from Minneapolis,
Minnesota to Charlotte, South Carolina.
What is this time in hours?
16. Muriel completed her math test in
2,100 seconds. What is this time in
minutes?
Grade 5
29
Chapter 11
Date
Skills Practice
Problem-Solving Investigation: Choose the Best Strategy
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Use any strategy to solve each problem.
1. Courtney rode her bike 3 miles east to
the library. She then rode 2 miles north
to the park. Finally, she rode 1 mile
west, and 1 mile south. How far east
of her original position was Courtney
at the end?
2. Siri has one box of crayons that
weighs 7 ounces, one box of crayons
that weighs 23 ounces, and 2 boxes
of crayons that weigh 15 ounces.
Estimate how many pounds of crayons
Siri has.
3. Melissa and Jack are putting pencils
into boxes. For every 6 yellow pencils,
they put half as many red pencils.
If they put 18 pencils into a box
altogether, how many are red?
4. Jonas needs to bring 38 pints of water
on his camping trip. He plans to bring
this water in gallon jugs. How many
jugs will he need?
5. Marco works on the computer for
28 minutes on Monday, 37 minutes
on Tuesday, and 46 minutes on
Wednesday. If he continues this
pattern, how many minutes will he
work on the computer for on Saturday?
6. Jasmine is baking banana bread. Her
recipe says that she can make 2 loaves
with one pint of milk. How many
loaves can she make with a gallon
of milk?
Grade 5
35
Chapter 11
Chapter Resources
11–6
Name
Date
Skills Practice
Elapsed Time
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Find each elapsed time.
1. 3:15 P.M. to 8:30 P.M.
2. 5:55 P.M. to 11:58 P.M.
3. 6:24 A.M. to 10:30 A.M.
4. 9:12 P.M. to 10:55 P.M.
5. 2:13 P.M. to 7:45 P.M.
6. 1:15 P.M. to 4:29 P.M.
7. 7:30 P.M. to 9:55 P.M.
8. 2:15 A.M. to 2:20 P.M.
9. 5:45 P.M. to 12:30 A.M.
10. 6:10 A.M. to 11:05 A.M.
11. 1:12 P.M.to 10:45 P.M.
12. 8:10 P.M. to 12:50 A.M.
13. 3:24 A.M. to 8:19 A.M.
14. 1:19 P.M. to 5:35 P.M.
15. 4:07 P.M. to 6:10 P.M.
16. 6:30 P.M. to 10:55 P.M.
17. 5:15 A.M. to 12:20 P.M.
18. 7:45 P.M. to 11:45 P.M.
19. 9:15 A.M. to 5:30 P.M.
20. 8:16 P.M. to 4:00 A.M.
21. 9:55 P.M. to 1:55 A.M.
22. 10:24 A.M. to 11:40 A.M.
23. 4:12 P.M. to 5:55 P.M.
24. 9:49 P.M. to 11:39 P.M.
25. Eric finished his homework at 7:48 P.M. and Marcus finished at 9:25 P.M. How many
minutes faster was Eric than Marcus?
26. Erin started exercising at 4:45 P.M. She finished exercising 80 minutes later. At what
time did she finish exercising?
Grade 5
39
Chapter 11
Chapter Resources
11–7
Name
12–1
Name
Date
Skills Practice
Chapter Resources
Units of Length
Select an appropriate unit to measure the length of each of the
following. Write millimeter, centimeter, meter, or kilometer.
1. length of your arm
2. thickness of a penny
3. length of a bus
4. height of a mountain
5. distance from your home to school
6. length of a shoelace
7. length of a canoe
8. height of a diving board
Complete.
9. 40 mm =
cm
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12. 21,000 m =
10. 10 km =
m
11. 50 mm =
km 13. 8,000 mm =
15. 5 km =
m
16. 7 km =
18. 45 m =
cm
19. 5,000 m =
m
m
cm
22. 90 mm =
24. 200 cm =
m
25. 49,000 m =
14. 3,000 m =
km
17. 60 mm =
km
21. 60 mm =
cm
cm
20. 18 m =
cm
mm
23. 7,000 m =
km 26. 8 m =
km
cm
Solve.
27. Kay is reading a book. Is the book’s
thickness more likely to be 19 mm or
19 km?
Grade 5
28. Scott kicked a football. Is the distance
he kicked it more likely to be 35 m or
35 km?
9
Chapter 12
Date
Skills Practice
Problem-Solving Strategy: Determine Reasonable Answers
Is each estimate reasonable? Explain.
1. Sandra needs to buy a phone cord that will reach a distance of at
least 12 yards. At the store, all of the packages are marked in feet.
Sandra estimates that the package with 40 feet of cord will be
enough. Is her estimate reasonable?
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. Kyle and Julie are watching a television program on weightlifting. A
man is going to lift 210 pounds. Julie comments that he is going to
lift 4,000 ounces. Is her estimate reasonable?
3. Ryan and Tyler are going to the pet shop to buy 12 cans of dog
food. They are trying to decide whether they should take their
wagon to help carry the dog food home. The cans weigh 15 ounces
each. They estimate that the dog food will weigh 10 pounds. Is the
estimate reasonable?
4. Nicole is trying out a new recipe. The recipe calls for 4 pints of
broth. Nicole has only a 1-cup measuring cup. She estimates that
she will need 16 cups of broth. Is her estimate reasonable?
Grade 5
15
Chapter 12
Chapter Resources
12–2
Name
12–3
Name
Date
Skills Practice
Chapter Resources
Units of Mass
Complete.
1. 7,000 g =
3. 4,000 mg =
g
g
4. 13 kg =
g
mg
5. 1.5 kg =
g
6. 46 g =
7. 65 kg =
g
8. 1,600 g =
kg
10. 4,000 g =
kg
9. 5,000 mg =
11. 7 kg =
Replace
12. 520.8 g
14. 295 g
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. 3,000 mg =
kg
g
g
with <, >, or = to make a true statement.
5,208 mg
29.5 kg
13. 320 g
3.2 kg
15. 6.34 g
63.4 mg
16. 4,300 g
0.43 kg
17. 0.9 g
18. 2.45 kg
245 g
19. 0.384 g
900 mg
3,840 mg
Solve.
20. Marc was telling his friends about
his new baby sister. Is her mass
more likely to be 40 milligrams or
4 kilograms?
Grade 5
21. Gavin likes to hold his pet cat, Shadow.
Is Shadow’s mass more likely to be
6 kilograms or 6 grams?
19
Chapter 12
12–4
Name
Date
Skills Practice
Units of Capacity
Complete.
1. 46 L =
2. 602 L =
mL
3. 7 L =
mL
5. 93 L =
mL
4. 350 mL =
L
mL
6. 13.5 L =
mL
7. 56 mL =
L
8. 19 mL =
L
9. 12 mL =
L
10. 3.07 L =
mL
mL
12. 4.2 mL =
L
13. 62 mL =
L
14. 6,400 L =
mL
15. 25 mL =
L
16. 1,500 mL =
11. 0.3 L =
17. 8.2 L =
19. 20.8 L
22. 6.3 L
25. 129 mL
18. 900 L =
mL
with <, >, or = to make a true statement.
208 mL
63 mL
12.9 L
20. 20 mL
0.2 L
23. 2,000 mL
26. 56.8 L
20 L
568 mL
21. 95 mL
24. 4.027 L
27. 3,000 mL
9.5 L
4,027 mL
0.03 L
Solve.
34. Jacob has 0.5 L of milk to use in two recipes. Each recipe uses
300 mL. Does he have enough? Explain.
Grade 5
24
Chapter 12
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Replace
mL
L
12–5
Name
Date
Skills Practice
Chapter Resources
Integers and Graphing on Number Lines
Write an integer to represent each situation. Then graph the
integer on a number line.
1. spent $15
2. 11 degrees colder than 0°F
3. 8 yard gain in football
4. deposit of $25 into an account
5. 10 feet below sea level
6. 3 centimeter increase in height
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write an integer to represent each situation. Then write its opposite.
7. withdrawal of $50 from bank account
8. received $5 allowance
9. speed increase of 15 mph
10. 30 seconds before lift-off
Describe a situation that can be represented by the integer.
11. -17
12. +$27
13. +45
14. -9
Grade 5
29
Chapter 12
12–6
Name
Date
Skills Practice
Units of Temperature
Fahrenheit
Celsius
212˚
boiling
100˚
98.6˚
body temperature
hot summer day
37˚
90˚
60˚
spring day
16˚
32˚
freezing point
0˚
32˚
Choose the more reasonable temperature for each situation.
Use the above thermometers if needed.
2. cup of hot chocolate: 75°C or 25°C
3. warm day: 27°C or 27°F
4. glass of cold milk: 55°C or 55°F
5. icy day: 40°F or 65°F
6. body temperature: 98°F or 198°F
Find each change in temperature. Use an integer to
represent the change.
7. 77°F to 90°F
8. 21°C to 0°C
9. 35°F to 79°F
10. 14°C to 26°C
11. 78°F to 24°F
12. 22°C to 17°C
Grade 5
34
Chapter 12
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. comfortable room temperature: 68°C or 68°F
12–7
Name
Date
Skills Practice
Problem-Solving Investigation: Choose the Best Strategy
Use any strategy to solve each problem.
2. Michael needs to arrive at school at
8:15 A.M. It takes him 20 minutes to
walk to school, 15 minutes to eat
breakfast, and 50 minutes to get
ready. What time does he need to set
his alarm clock for to get to school on
time?
1. Matt bought a tennis racket that
usually costs $73.95. He had a coupon
for a discount of d dollars. The net
price of the racket with the discount
was c dollars. Write an equation to
find the cost after the discount.
3. Joel, Santiago, and Tiffani each have
a different pet: a hamster, a dog, and
some fish. Joel likes to play fetch with
his pet and Santiago does not own the
dog or the fish. Who owns which pet?
4. Emile is thinking of three consecutive
numbers that add up to 75. What are
the numbers?
Grade 5
6. At Joseph’s birthday party, everyone
shook hands with everyone else. If
there were a total of 21 handshakes,
how many people were at the party?
40
Chapter 12
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Brooke is making a necklace in which
the first, fifth, ninth, and thirteenth
beads are blue and the rest of the first
15 beads are not blue. If the necklace
continues this pattern and has
50 beads in all, how many of them
will be blue?
13–1
Name
Date
Skills Practice
Chapter Resources
Geometry Vocabulary
Use each figure to determine if the pair of lines is parallel,
intersecting, or perpendicular. Choose the most specific term.
1.
2.
3.
Use the figure for Exercises 4–6.
K
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
J
D
E
A
B
I
F
G
C
H
4. Name a pair of parallel lines.
5. Name two pairs of perpendicular lines.
6. Name a pair of intersecting lines.
Grade 5
9
Chapter 13
Date
Skills Practice
Problem-Solving Strategy: Use Logical Reasoning
1. Of 26 people surveyed, 19 said they
go to basketball games and 12 said
they go to football games. Five of the
people said they go to both. How
many people said they go to basketball
games, but not to football games?
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. Of 24 students surveyed, 17 students
said they like board games and 12
said they like card games. Five students
said they like both. How many
students said they like board games,
but not card games?
5. Nathan wants to buy trading cards.
Superstar packages cost $3.23 each
and mixed packages cost $1.78 each.
Nathan buys 7 packages and spends
a total of $15.36. How many of each
type of package did he buy?
4. Of the 50 people surveyed at a
recreation center, 32 said they used
the basketball courts and 24 said
they used the racquetball courts. Six
of the people said they used both
courts. How many people said they
use the racquetball courts, but not the
basketball courts?
6. An after-school club is building a
clubhouse that is 8 feet by 6 feet. They
are also including a trampoline with a
radius of 4 feet. What is the total area
of the clubhouse and the trampoline,
to the nearest square foot?
7. A band is performing on a rectangular
stage that is 36 feet by 24 feet. The
manager wants to set up lights every
4 feet around the stage, including the
corners. How many lights will he need?
Grade 5
2. Of 40 teachers surveyed, 34 said
they listen to classical music and 17
said they listen to opera. Eleven of
the teachers said they listen to both
classical music and opera. How many
teachers listen to classical music, but
not to opera?
15
8. Write a problem that you could use
logical reasoning to solve. Share it with
a classmate.
Chapter 13
Chapter Resources
13–2
Name
Name
13–3
Date
Skills Practice
Chapter Resources
Triangles
Classify each triangle as acute, right, or obtuse. Then classify each
triangle as scalene, isosceles, or equilateral.
1.
2.
3.
20°
x
30°
The sum of the measures of the angles of a triangle is 180º. Find the
value of x in each triangle drawn or having the given angle measures.
4.
76º
x˚
5.
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
40º
71º
62º
x˚
7. 60°, 60°, x°
6.
80º
8. x°, 120°, 30°
x˚
40º
9. 50°, 115°, x°
Solve.
11. Amber draws an obtuse triangle with
10. Tyler draws a triangle with a 35° angle
and an 85° angle. What is the measure
of the third angle?
Grade 5
a 110° angle. The other two angles are
congruent. What are the measures of
the other two angles?
19
Chapter 13
13–4
Name
Date
Skills Practice
Quadrilaterals
What term best describes each quadrilateral?
1.
2.
3.
Determine whether each statement is sometimes, always, or never
true. Explain your reasoning.
4. A square is a rhombus.
5. A trapezoid has exactly one pair of
congruent sides.
Solve. The sum of the measures of the angles of a quadrilateral is 360º.
7. Lee drew a quadrilateral with three
angles that measure 120 degrees,
110 degrees, and 70 degrees. What is
the measure of the fourth angle?
Grade 5
8. Robert drew a parallelogram with
two 55-degree angles. What are the
measures of the other two angles?
24
Chapter 13
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6. A rhombus is a parallelogram.
13–5
Name
Date
Skills Practice
Problem-Solving Investigation: Choose the Best Strategy
Use any strategy shown below to solve each problem.
• Look for a pattern
• Draw a diagram
• Guess and check
Use the picture to answer Exercises 1 and 2.
1. Suppose there are 125 marbles in the jar on the right and
25 marbles in the jar on the left. Write a fraction to show the empty
part of the first container. Assume the jar on the right is full.
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. What fraction represents the difference between the amounts in
each container?
3. In 2006 you sold 25 rolls of wrapping paper for a fundraiser. In
2007 you sold 30 rolls. If the trend continues, how many rolls will
you sell in 2008?
4. Look at the pattern below. What are the next three bugs?
Ladybug, ladybug, bee, ant, ladybug, ladybug, bee, ant, ladybug
Grade 5
30
Chapter 13
Name
13–6
Date
Skills Practice
Translations and Graphs
A triangle has vertices (3, 4), (5, 6), and (6, 3). Graph the triangle. Then
graph the image after each translation. Then write the ordered pairs for
the new vertices.
1. 3 units right
9
8
7
6
5
4
3
2
1
0
2. 4 units up
3. 1 unit left, 3 units down
9
8
7
6
5
4
3
2
1
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9
0
0
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
5. triangle FGH with vertices F(5, 5),
G(5, 9), H(8, 5); translated 3 units left,
1 unit down
4. quadrilateral ABCD with vertices
A(0, 2), B(2, 6), C(5, 6), D(3, 2);
translated 4 units right
9
8
7
6
5
4
3
2
1
0
Grade 5
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9
0
34
1 2 3 4 5 6 7 8 9
Chapter 13
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Graph each figure and the translation described. Write the ordered
pairs for the new vertices.
Date
Skills Practice
Reflections and Graphs
Graph each figure after a reflection across the line. Then write the ordered pairs
for the new vertices.
1.
0
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3.
1 2 3 4 5 6 7 8 9
4.
1 2 3 4 5 6 7 8 9
6.
Grade 5
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
9
8
7
6
5
4
3
2
1
0
39
1 2 3 4 5 6 7 8 9
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
9
8
7
6
5
4
3
2
1
0
5.
2.
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9
Chapter 13
Chapter Resources
13–7
Name
13–8
Name
Date
Skills Practice
Rotations and Graphs
For Exercises 1–3, graph triangle ABC. Then graph the rotation image. Write the
ordered pairs for the new vertices.
1. 90° counterclockwise about point A
9
8
7
6
5
4
3
2
1
0
A
9
8
7
6
5
4
3
2
1
B
C
0
1 2 3 4 5 6 7 8 9
3. 90° counterclockwise about point C
9
8
7
6
5
4
3
2
1
0
Grade 5
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9
0
44
1 2 3 4 5 6 7 8 9
Chapter 13
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. 180° clockwise about point A
1 2 3 4 5 6 7 8 9
Date
Skills Practice
Identify Transformations
Determine whether each transformation is a translation, reflection, or rotation.
1.
0
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7.
2.
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9
0
0
8.
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9
6.
9
8
7
6
5
4
3
2
1
0
0
1 2 3 4 5 6 7 8 9
9.
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9
9
8
7
6
5
4
3
2
1
0
1 2 3 4 5 6 7 8 9
Solve.
10.
Which uppercase letters look like different uppercase letters when they are
reflected over a horizontal line?
11.
You can transform a lowercase v in two different ways so that the v and its
transformations form other lowercase letters. Describe the transformations and tell
what letters you would form.
Grade 5
49
Chapter 13
Chapter Resources
13–9
Name
Name
14–1
Date
Skills Practice
Chapter Resources
Perimeters of Polygons
Find the perimeter of each figure.
2.
1.
7 cm
7m
4 cm
3 cm
5m
3.
4 in.
4.
5 in.
8 in.
4 in.
5 cm
6 in.
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10 in.
5.
3 cm
3 cm
3 cm
7 cm
6.
2 in.
9m
2 in.
2 in.
9m
6 in.
Solve.
8. Molly has 60 feet of fencing to go
around the perimeter of her garden.
She wants the garden to be a square.
How long should each side be?
7. Find the perimeter of an isosceles
triangle whose sides are 8 inches and
whose base is 4 inches.
Grade 5
9
Chapter 14
14–2
Name
Date
Skills Practice
Area
Estimate the area of each figure. Each square represents 1 square
centimeter.
1.
2.
A=
4.
3.
A=
A=
5.
7.
A=
A=
8.
A=
Grade 5
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A=
6.
9.
A=
A=
14
Chapter 14
14–3
Name
Date
Skills Practice
Chapter Resources
Areas of Rectangles
Find the area of each rectangle or square.
1.
2.
3.
4 in.
16 cm
9 ft
8 in.
21 cm
9 ft
A=
A=
4.
A=
5.
6.
35 m
35 m
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
25 in.
63 cm
25 in.
17 cm
A=
A=
A=
Find each missing measurement.
7.
8.
9.
z
b
4 in.
12 cm
p in.
b
A = 48 square centimeters
z=
A = 16 square feet
A = 72 square inches
b=
p=
Solve.
10. A family room is 24 feet long and
18 feet wide. What is the area of the
family room?
Grade 5
11. A square carpet is 36 meters on each
side. What area will the carpet cover?
19
Chapter 14
14–4
Name
Date
Skills Practice
Geometry: Three-Dimensional Figures
Describe parts of each figure that are parallel and congruent. Then
identify the figure.
1.
2.
3.
Describe parts of each figure that are perpendicular and
congruent. Then identify the figure.
4.
5.
6.
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve.
7. Describe the number of faces, vertices and edges in a can of soup.
Identify the shape of the can.
Grade 5
24
Chapter 14
14–5
Name
Date
Skills Practice
Problem-Solving Strategy
Solve. Use the make a model strategy.
1. Ping and Kuri are designing a small end table using 1-inch tiles.
If Kuri picks three times as many tiles out than Ping, and Ping picks
out 24 tiles, how many total tiles are there? The area of the table is
19 inches by 5 inches. Will they have enough tiles to cover the tabletop?
2. The Miller family is redoing their garden. If they have a garden that
is 500 square feet, and one side is 10 feet long, what is the length
of the other side of the garden? If they plant 5 trees that need to be
5 feet apart and 5 feet away from the fence around the garden, will
they have the space?
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. Bob is organizing his pantry. If he has cracker boxes that measure
12 inches high, 2 inches wide, and 10 inches long, how many
boxes can he fit on a 24-inch-long shelf that is 14 inches deep?
4. You are packing picnic baskets for a day camp. Each basket needs
to carry 8 square sandwiches, 8 apples, and 8 juice boxes. Would
the best basket be an 18” × 15” × 9” basket, a 72” × 40” × 18”
basket, or a 12” × 6” × 8” basket?
5. Roberto wants to build a long train track. If each piece of track is
6 inches long, and he has 42 pieces, can he make a track that is
20 feet long? Can he make a track that is 22 feet long?
Grade 5
30
Chapter 14
14–6
Name
Date
Skills Practice
Volume of Prisms
Find the volume of each prism.
2.
1.
V=
3.
V=
4.
V=
5.
10 ft
6.
16 cm
12 m
32 ft
20 m
16 cm
9 ft
16 cm
V=
12 m
V=
V=
9.
7m
17 in.
25 in.
2m
50 cm
65 cm
40 cm
9m
8 in.
V=
V=
V=
Solve.
10. The dimensions of a gift box for
jewelry are 6 inches by 3 inches by
2 inches. What is the volume of the
gift box?
Grade 5
11. The dimensions of a shoe box are
13 inches by 9 inches by 4 inches.
What is the volume of the shoe box?
34
Chapter 14
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8.
7.
14–7
Name
Date
Skills Practice
Chapter Resources
Surface Areas of Prisms
Find the surface area of each rectangular prism.
2.
1.
3.
4.
5.
16 cm
11 in.
15 cm
10 in.
16 cm
12 in.
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
16 cm
25 cm
9 cm
6.
7.
8.
1.5 m
20 cm
10 in.
3 in.
10 cm
5.2 cm
0.9 m
2m
3 in.
Problem Solving
Solve.
9. What is the surface area of a cardboard
shipping box that is 26 inches long, 26
inches wide, and 18 inches high?
Grade 5
10. What is the surface area of a
9-centimeter cube?
39
Chapter 14
14–8
Name
Date
Skills Practice
Select Appropriate Measurement Formulas
Determine whether you need to find the perimeter, area, or volume. Then solve.
1. Hayden wants to make a rectangular herb garden that is 4 feet long and 3 feet wide.
She wants to plant lavender in half of the garden. How much of the garden will be
covered with lavender?
2. Daniel wants to plant a row of marigolds along the border of his vegetable garden.
The garden is 6 feet long and 4 feet wide. How much of the garden will need to be
covered with marigolds?
3. Ms. Carmichael is building a deck with two levels. The lower level is a square. The
length of each side is 5 feet. The upper level is rectangular in shape, 12 feet long and
8 feet wide. How much wood will she need to construct each level?
5. Jamison has 70 square feet of plywood to make a floor for a two-room clubhouse he
is building. The floor of one room is 8 feet long and 6 feet wide. The floor of the other
room is 5 feet long and 4 feet wide. How can he decide if he has enough plywood?
6. Amy wants to make a frame for a painting that is 24 inches long and 18 inches wide.
She found a wood molding she would like to use. How can she decide how much
molding she needs to make the frame?
Grade 5
44
Chapter 14
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. Ms. Carmichael wants to use the space underneath the lower level as storage space.
If the lower level of the deck is 4 feet high off the ground, how much storage space
will she have?
14–9
Name
Date
Skills Practice
Problem-Solving Investigation: Choose the Best Strategy
Use any strategy shown below to solve each problem.
• Make a model
• Draw a diagram
• Look for a pattern
• Use logical reasoning
1. A pet store is building new cages for their birds. They have
8 cockatiels, 32 parakeets, and 28 finches. How many cages will
they need if each cage will hold either 2 cockatiels, 10 parakeets, or
14 finches. The different types of birds are all kept separate.
2. You decide to do an even exchange on an outfit that you received
for your birthday. The top and pants total $32. If you pick another
top for $14, how much is the highest price of the pants, that you
can pick out?
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. Danielle picks fruit from her family’s lemon tree. She picked
28 lemons. If each lemon makes _12_ cup of lemonade after
adding water, how many cups of lemonade can she make?
4. Meredith is making a dress. She has 5 feet of ribbon. She needs
12 inches of ribbon for the neck and two 6-inch pieces for the cuffs.
How many cuts will she need to make to get 6 equal lengths from
the rest of the ribbon for bows?
5. Taye ran for 3 miles each week. On each fourth week, he ran an
extra mile. How many miles did he run after 4 weeks? How many
miles did he run after 7 weeks?
Grade 5
50
Chapter 14
Date
Skills Practice
Probability
List the possible outcomes in each probability experiment.
1. spinning the spinner
1
2. Selecting a marble from the bag
without looking.
2
1
2
3. spinning the spinner without looking
G
4. randomly choosing a card
2 3 5
A
1
6
8
6
3
8
3 4 3
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Y
Y
B G
Y
R
Y
G
R
B
R
1
P
E
Q
A
One card is drawn without looking. Describe the probability of drawing each card. Write
certain, impossible, unlikely, equally likely or likely.
5. Picking a circle rather than a square
6. Picking a square rather than a triangle
7. Picking a pentagon
Solve.
8. Two girls and three boys want to borrow the same book from the school library.
Each writes his or her name on a card. If the librarian picks a card at random,
describe the probability that a girl will be chosen to borrow the book.
Grade 5
9
Chapter 15
Chapter Resources
15–1
Name
15–2
Name
Date
Skills Practice
Probability as a Fraction
One shape is selected from the shapes shown. Find the probability
of each event. Write as a fraction in simplest form.
1. P(quadrilateral)
2. P(shape with a pattern)
3. P(shape with polka dots)
4. P(shape with no edges)
5. P(shape with a vertex)
One marble is picked from the bag. Find the probability of each
event. Write as a fraction in simplest form.
G
7. P(red, yellow, blue, or green)
B
B
B
8. P(green)
Y
Y
Y
R
Y
B
B
R
R
R
9. P(red or yellow)
10. P(blue or green)
Grade 5
14
Chapter 15
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6. P(red)
15–3
Name
Date
Skills Practice
Problem-Solving Strategy: Make an Organized List
Solve by making an organized list.
2. Jackson is making a sandwich. He
can choose from ham, turkey, or roast
beef, wheat, white, or rye bread, and
mayonnaise or mustard. How many
different sandwiches can he make?
Hint: Choose only one meat, one
bread, and one condiment.
3. Allie has square beads that are red,
blue, and green. She has round beads
that are yellow and white. If she
chooses one color from each shape of
beads, how many different possibilities
of colors can she have?
4. Ms. Dawson eats a fruit and a
vegetable for lunch each day. She
selects an apple, a banana, an orange,
or a pear for her fruit. She chooses
carrot sticks, celery sticks, or green
pepper slices for her vegetable. How
many different ways can she choose
1 fruit and 1 vegetable?
5. There are three girls, Jackie, Janey, and
Janelle. How many different ways can
the girls be lined up?
6. Greta orders stickers that come with
12 sheets per package. Each sheet has
10 rows of stickers and each row has
8 stickers. How many stickers are in
each package?
Grade 5
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Chapter 15
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1. Tom has a blue shirt, a red shirt, and
a yellow shirt. He also has a pair of
blue jeans, a pair of khaki pants, and a
pair of corduroys. How many different
outfits are possible if he chooses one
shirt and one pair of pants?
15–4
Name
Date
Skills Practice
Counting Outcomes
Use a tree diagram to find the possible outcomes.
1. How many choices do you have for your lunch if you pick either an
orange or apple and pretzels or carrots to go with your sandwich?
2. You have a friend over to play. You decide to play cards, have
a snack, and watch a movie. How many different ways can you
complete your activities?
3. You are getting ready for school and you only have a choice of a
white, purple, or blue shirt and either a pair of jeans, shorts, or a
skirt. How many possible outfits can you have?
1
5
2
4
3
4. Find the number of possible outcomes.
5. Find the probability of tossing a four
and spinning a number less than 3.
6. Find the probability of tossing
a 1 and spinning a 3.
7. Find the probability of tossing an even
number and spinning a number less
than 5.
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Chapter 15
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
For the following exercises, toss a number cube and spin the
spinner shown.
15–5
Name
Date
Skills Practice
Problem-Solving Investigation: Choose the Best Strategy
Use any strategy shown below to solve each problem.
• Look for a pattern.
• Work backward.
• Solve a simpler problem.
1. Digna packed up 10 dinners to deliver to the food shelter. Isabel
packed twice as many dinners as Digna. Rosa packed _14_ the amount
of meals as Isabel. Juanita packed three times as many dinners as
Rosa. How many dinners in all did the girls prepare? Who prepared
the most dinners? Who prepared the least number of dinners?
2. Refer to question number 1. If it takes the girls 1 hour to deliver 5
meals, in how many hours will they deliver all of the meals? If they
break up into two groups, with 2 girls in each group and work at
the same rate, how long will it take them to deliver the meals?
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. For every dollar Luisa puts into her savings account, her parents
put in $0.50. If Luisa put $40 a week into her savings account, how
much will she have saved up at the end of the month?
4. Keshia bought a new outfit. She chooses a top that cost $48.95 and
leather boots that were twice as much as the top. The pants were
one third of the price of the boots. If she received $20.52 back in
change, how much money did she give to the cashier?
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Chapter 15